Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D3×D4 |
| commutator, cosocle | C2×C3×C4 | C24 |
| Frattini | C2×C4 | C23×D3 |
| Fitting | C3×#467 | C2 |
| socle | C22×C3 | C22×D4 |
| hypercenter | #467 | D3 |
| hypocenter | C3 | #3283 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #467 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#919 | C2 | semidirect |
| 2. C2×#904 | C2 | semidirect |
| 3. #5631 | C2 | semidirect |
| 4. C3×#467 | C2 | semidirect |
| 5. #5183 | C2 | semidirect |
| 6. C8×#67 | C2 | semidirect |
| 7. #5047 | C2 | semidirect |
| 8. #4887 | C2 | semidirect |
| 9. #4872 | C2 | semidirect |
| 10. #4818 | C2 | semidirect |
| 11. #4808 | C2 | semidirect |
| 47. #467 | D3 | semidirect |
| 89. D24 | D4 | semidirect |
| 209. Dic3 | #135 | semidirect |
| 266. C3 | #3283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#919 | 2 |
| C2×#904 | 2 |
| #5631 | 2 |
| C3×#467 | 2 |
| #5183 | 2 |
| C8×#67 | 2 |
| #5047 | 2 |
| #4887 | 2 |
| #4872 | 2 |
| #4818 | 2 |
| #4808 | 2 |
| #3283 | 3 |