Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×#67 |
| commutator, cosocle | C2×C3×C4 | C24 |
| Frattini | C2×C4 | C23×D3 |
| Fitting | C3×#535 | C2 |
| socle | C22×C3 | C22×D4 |
| hypercenter | #535 | D3 |
| hypocenter | C3 | #3045 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #535 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#535 | C2 | semidirect |
| 2. C2×#950 | C2 | semidirect |
| 3. C2×#932 | C2 | semidirect |
| 4. #5523 | C2 | semidirect |
| 5. #5232 | C2 | semidirect |
| 6. C2×#832 | C2 | semidirect |
| 7. #5075 | C2 | semidirect |
| 8. #5072 | C2 | semidirect |
| 9. #5057 | C2 | semidirect |
| 10. #5054 | C2 | semidirect |
| 11. #4999 | C2 | semidirect |
| 23. C2×#216 | C22 | semidirect |
| 24. C2×#215 | C22 | semidirect |
| 26. C2×#214 | C22 | semidirect |
| 29. C2×#213 | C22 | semidirect |
| 36. C4×D12 | C22 | semidirect |
| 37. C4×Dic6 | C22 | semidirect |
| 38. #835 | C22 | semidirect |
| 41. #832 | C22 | semidirect |
| 42. C4⋊(C3⋊C8) | C22 | semidirect |
| 43. C4⋊(C3⋊C8) | C22 | semidirect |
| 46. #535 | D3 | semidirect |
| 72. #235 | D4 | semidirect |
| 301. C3 | #3045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#535 | 2 |
| C2×#950 | 2 |
| C2×#932 | 2 |
| #5523 | 2 |
| #5232 | 2 |
| C2×#832 | 2 |
| #5075 | 2 |
| #5072 | 2 |
| #5057 | 2 |
| #5054 | 2 |
| #4999 | 2 |
| #3045 | 3 |