Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
322 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 322 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×#432 | C2 |
| prime radical | C23×C3 | C22×C4 |
| cosocle | C2×C3×C4 | C24 |
| hypercenter | #432 | D3 |
| hypocenter | C3 | #2985 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ #432 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #4831 | C2 | semidirect |
| 5. #4830 | C2 | semidirect |
| 7. #4701 | C2 | semidirect |
| 158. C3 | #2985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5470 | 2 |
| C3×#432 | 2 |
| #4925 | 2 |
| #4831 | 2 |
| #4830 | 2 |
| #4720 | 2 |
| #4701 | 2 |
| #2985 | 3 |