Finite Group DatabasebetaFinite Group DatabasebetaOrder 396.
36 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C32×C11 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Dic33 | — | 3 | 4 | no | maximal |
| 3 | C32×C11 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C2×C3×C11 | D3 | 1 | 4 | yes | — |
| 5 | Dic11 | — | 9 | 1 | no | Hall |
| 6 | C3⋊Dic3 | — | 11 | 1 | no | maximal, Hall |
| 7 | C3×C11 | Dic3 | 1 | 4 | yes | complemented |
| 8 | C2×C11 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 9 | C2×C32 | D11 | 1 | 1 | yes | characteristic |
| 10 | Dic3 | — | 33 | 4 | no | — |
| 11 | C11 | C3⋊Dic3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C32 | Dic11 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | C2×C3 | D33 | 1 | 4 | yes | — |
| 14 | C4 | — | 99 | 1 | no | Sylow |
| 15 | C3 | Dic33 | 1 | 4 | yes | complemented |
| 16 | C2 | C3⋊D33 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D33 |
| commutator, hypocenter | C32×C11 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C32×C11 | C2 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C32×C11 | C4 | semidirect |
| 7. C3×C11 | Dic3 | semidirect |
| 11. C11 | C3⋊Dic3 | semidirect |
| 12. C32 | Dic11 | semidirect |
| 15. C3 | Dic33 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C11 | 2 |
| Dic33 | 3 |
| C3⋊Dic3 | 11 |