Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#895 |
| commutator, cosocle | C2×C3×C4 | C24 |
| Frattini | C2×C4 | C23×D3 |
| Fitting | C3×#430 | C2 |
| socle | C2×C3 | C2×#121 |
| hypercenter | #430 | D3 |
| hypocenter | C3 | #3068 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #430 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #5748 | C2 | semidirect |
| 2. C2×#908 | C2 | semidirect |
| 3. C2×#908 | C2 | semidirect |
| 4. #5745 | C2 | semidirect |
| 5. C3×#430 | C2 | semidirect |
| 6. #5132 | C2 | semidirect |
| 7. C2×#823 | C2 | semidirect |
| 8. #4898 | C2 | semidirect |
| 9. #4897 | C2 | semidirect |
| 19. #909 | C22 | semidirect |
| 25. #908 | C22 | semidirect |
| 30. C2×D24 | C22 | semidirect |
| 32. C2×#204 | C22 | semidirect |
| 33. #901 | C22 | semidirect |
| 34. C3×#108 | C22 | semidirect |
| 35. #824 | C22 | semidirect |
| 36. #823 | C22 | semidirect |
| 37. #823 | C22 | semidirect |
| 44. #430 | D3 | semidirect |
| 116. #108 | C2×D3 | semidirect |
| 287. C3 | #3068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5748 | 2 |
| C2×#908 | 2 |
| #5745 | 2 |
| C3×#430 | 2 |
| #5132 | 2 |
| C2×#823 | 2 |
| #4898 | 2 |
| #4897 | 2 |
| #3068 | 3 |