Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
944 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 163 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, socle, cosocle | C23×C3 | C24 |
| Fitting | C3×#393 | C2 |
| hypercenter | #393 | D3 |
| hypocenter | C3 | #2388 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#239 | C2 | semidirect |
| 2. C2×#67⋊C4 | C2 | semidirect |
| 3. C3×#393 | C2 | semidirect |
| 4. #5230 | C2 | semidirect |
| 5. #4960 | C2 | semidirect |
| 6. #4672 | C2 | semidirect |
| 7. #4666 | C2 | semidirect |
| 27. #393 | D3 | semidirect |
| 46. C2×C4×D3 | D4 | semidirect |
| 68. C23×C3 | #41 | semidirect |
| 86. C2×Dic3 | #41 | semidirect |
| 134. C23 | #239 | semidirect |
| 171. C3 | #2388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#239 | 2 |
| C2×#67⋊C4 | 2 |
| C3×#393 | 2 |
| #5230 | 2 |
| #4960 | 2 |
| #4672 | 2 |
| #4666 | 2 |
| #2388 | 3 |