Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D3 |
| commutator | C22×C3 | C23×C4 |
| Fitting | C3×#376 | C2 |
| socle, cosocle | C23×C3 | C24 |
| prime radical | C22×D12 | C22 |
| hypercenter | #376 | D3 |
| hypocenter | C3 | #2372 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#376 | C2 | semidirect |
| 3. #4940 | C2 | semidirect |
| 4. C4×(C2×D3)⋊C4 | C2 | semidirect |
| 5. #4932 | C2 | semidirect |
| 6. #4669 | C2 | semidirect |
| 7. #4666 | C2 | semidirect |
| 9. #4646 | C2 | semidirect |
| 24. #875 | C4 | semidirect |
| 41. #376 | D3 | semidirect |
| 59. C2×Dic6 | C2×C4 | semidirect |
| 61. C3×C42 | C2×C4 | semidirect |
| 65. (C2×D3)⋊C4 | C2×C4 | semidirect |
| 66. (C2×D3)⋊C4 | C2×C4 | semidirect |
| 152. C42 | C4×D3 | semidirect |
| 232. C3 | #2372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#875 | 2 |
| C3×#376 | 2 |
| #4940 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| #4932 | 2 |
| #4669 | 2 |
| #4666 | 2 |
| #4665 | 2 |
| #4646 | 2 |
| #2372 | 3 |