Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
330 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D3 |
| commutator, socle | C22×C3 | C23×C4 |
| Fitting | C3×#433 | C2 |
| prime radical | C23×C3 | C22×C4 |
| cosocle | C2×C3×C4 | C24 |
| hypercenter | #433 | D3 |
| hypocenter | C3 | #2986 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ #433 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #4830 | C2 | semidirect |
| 5. #4828 | C2 | semidirect |
| 8. #4701 | C2 | semidirect |
| 9. C8×Dic6 | C2 | semidirect |
| 179. C3 | #2986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5517 | 2 |
| C3×#433 | 2 |
| #5000 | 2 |
| #4830 | 2 |
| #4828 | 2 |
| #4720 | 2 |
| #4718 | 2 |
| #4701 | 2 |
| C8×Dic6 | 2 |
| #2986 | 3 |