Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 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×#381 | C2 |
| socle, cosocle | C23×C3 | C24 |
| prime radical | C2×#930 | C2 |
| hypercenter | #381 | D3 |
| hypocenter | C3 | #2377 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#381 | C2 | semidirect |
| 3. #5212 | C2 | semidirect |
| 4. #4957 | C2 | semidirect |
| 5. #4956 | C2 | semidirect |
| 6. #4670 | C2 | semidirect |
| 7. #4668 | C2 | semidirect |
| 8. #4665 | C2 | semidirect |
| 9. #4654 | C2 | semidirect |
| 18. #930 | C4 | semidirect |
| 40. #381 | D3 | semidirect |
| 45. C22×C3×C4 | C2×C4 | semidirect |
| 52. C2×#67 | C2×C4 | semidirect |
| 67. (C2×D3)⋊C4 | C2×C4 | semidirect |
| 69. C4⋊Dic3 | C2×C4 | semidirect |
| 144. C22×C4 | C4×D3 | semidirect |
| 251. C3 | #2377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#930 | 2 |
| C3×#381 | 2 |
| #5212 | 2 |
| #4957 | 2 |
| #4956 | 2 |
| #4670 | 2 |
| #4668 | 2 |
| #4665 | 2 |
| #4654 | 2 |
| #2377 | 3 |