Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #5717 |
| commutator, cosocle | C2×C3×C4 | C24 |
| Frattini | C2×C4 | C23×D3 |
| Fitting | C3×#493 | C2 |
| socle | C2×C3 | D42 |
| hypercenter | #493 | D3 |
| hypocenter | C3 | #3292 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #493 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #5757 | C2 | semidirect |
| 2. C3×#493 | C2 | semidirect |
| 3. #5160 | C2 | semidirect |
| 4. #5077 | C2 | semidirect |
| 5. #4700 | C2 | semidirect |
| 7. #1004 | C22 | semidirect |
| 8. C2×C3×D8 | C22 | semidirect |
| 9. C3×#127 | C22 | semidirect |
| 10. #932 | C22 | semidirect |
| 15. #901 | C22 | semidirect |
| 16. C3×C4×C8 | C22 | semidirect |
| 17. #833 | C22 | semidirect |
| 18. #819 | C22 | semidirect |
| 19. #805 | C22 | semidirect |
| 21. #493 | D3 | semidirect |
| 38. Dic12 | D4 | semidirect |
| 39. D24 | D4 | semidirect |
| 40. #204 | D4 | semidirect |
| 49. C2×D8 | C2×D3 | semidirect |
| 51. #127 | C2×D3 | semidirect |
| 55. C4×C8 | C2×D3 | semidirect |
| 124. C3 | #3292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5757 | 2 |
| C3×#493 | 2 |
| #5160 | 2 |
| #5077 | 2 |
| #4700 | 2 |
| #3292 | 3 |