Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1202 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 491 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D3 |
| commutator, socle, cosocle | C22×C3 | C25 |
| Fitting | C3×Q82 | C2 |
| hypercenter | Q82 | D3 |
| hypocenter | C3 | #3483 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×Q82 | C2 | semidirect |
| 2. #5734 | C2 | semidirect |
| 3. #5725 | C2 | semidirect |
| 4. #5577 | C2 | semidirect |
| 5. C4×#239 | C2 | semidirect |
| 19. Q82 | D3 | semidirect |
| 52. C3×Q8 | #41 | semidirect |
| 84. Q8 | #239 | semidirect |
| 103. C3 | #3483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q82 | 2 |
| #5734 | 2 |
| #5725 | 2 |
| #5577 | 2 |
| C4×#239 | 2 |
| #3483 | 3 |