Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
1015 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C26 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 2 | C22⋊A4 | — | 4 | 21 | no | maximal |
| 3 | C25 | — | 3 | 21 | no | — |
| 4 | C24 | — | 3 | 210 | no | — |
| 5 | C24 | A4 | 1 | 21 | yes | complemented |
| 6 | A4 | — | 16 | 21 | no | — |
| 7 | C23 | — | 3 | 360 | no | — |
| 8 | C23 | — | 3 | 105 | no | — |
| 9 | C22 | — | 3 | 210 | no | — |
| 10 | C22 | C22⋊A4 | 1 | 21 | yes | complemented |
| 11 | C3 | — | 64 | 1 | no | Sylow |
| 12 | C2 | — | 3 | 21 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C26 | C3 |
| LCS | G ▷ C26 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C26 | C3 | semidirect |
| 5. C24 | A4 | semidirect |
| 10. C22 | C22⋊A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C26 | 3 |
| C22⋊A4 | 4 |