Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
258 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C3×C42 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C4×Dic3 | C2 | 1 | 6 | yes | maximal |
| 3 | C43 | — | 3 | 1 | no | maximal, Sylow |
| 4 | C22×C3×C4 | C22 | 1 | 3 | yes | — |
| 5 | C22×Dic3 | C22 | 1 | 4 | yes | — |
| 6 | C3×C42 | C4 | 1 | 4 | yes | complemented |
| 7 | C4×Dic3 | C4 | 1 | 24 | yes | direct product factor |
| 8 | C2×C42 | — | 3 | 6 | no | — |
| 9 | C2×C42 | D3 | 1 | 1 | yes | characteristic |
| 10 | C23×C3 | C23 | 1 | 1 | yes | characteristic |
| 11 | C2×C3×C4 | C2×C4 | 1 | 12 | yes | — |
| 12 | C2×C3×C4 | C2×C4 | 1 | 6 | yes | — |
| 13 | C2×Dic3 | C2×C4 | 1 | 24 | yes | — |
| 14 | C22×C4 | — | 3 | 4 | no | — |
| 15 | C22×C4 | C2×D3 | 1 | 3 | yes | — |
| 16 | C42 | — | 3 | 24 | no | — |
| 17 | C42 | Dic3 | 1 | 4 | yes | direct product factor |
| 18 | C22×C3 | C22×C4 | 1 | 6 | yes | — |
| 19 | C22×C3 | C22×C4 | 1 | 1 | yes | characteristic |
| 20 | C3×C4 | C42 | 1 | 12 | yes | complemented |
| 21 | Dic3 | C42 | 1 | 16 | yes | direct product factor |
| 22 | C23 | C22×D3 | 1 | 1 | yes | characteristic |
| 23 | C2×C4 | — | 3 | 24 | no | — |
| 24 | C2×C4 | C4×D3 | 1 | 12 | yes | — |
| 25 | C2×C4 | C2×Dic3 | 1 | 6 | yes | — |
| 26 | C2×C3 | C2×C42 | 1 | 4 | yes | — |
| 27 | C2×C3 | C2×C42 | 1 | 3 | yes | — |
| 28 | C22 | C2×C4×D3 | 1 | 6 | yes | — |
| 29 | C22 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 30 | C4 | — | 3 | 16 | no | — |
| 31 | C4 | C4×Dic3 | 1 | 12 | yes | direct product factor |
| 32 | C3 | C43 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 33 | C2 | C42×D3 | 1 | 4 | yes | — |
| 34 | C2 | C2×C4×Dic3 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D3 |
| commutator, hypocenter | C3 | C43 |
| Frattini | C23 | C22×D3 |
| Fitting | C2×C3×C42 | C2 |
| socle, prime radical, cosocle | C23×C3 | C23 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C3×C42 | C4 | semidirect |
| 7. C4×Dic3 | C4 | direct (N × H) |
| 17. C42 | Dic3 | direct (N × H) |
| 20. C3×C4 | C42 | semidirect |
| 21. Dic3 | C42 | direct (N × H) |
| 31. C4 | C4×Dic3 | direct (N × H) |
| 32. C3 | C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C42 | 2 |
| C2×C4×Dic3 | 2 |
| C43 | 3 |