Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 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 | C2×C3×#95 | C2 |
| prime radical | C24×C3 | C23 |
| hypercenter | C2×#95 | D3 |
| hypocenter | C3 | #2569 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. #4661 | C2 | semidirect |
| 7. #4660 | C2 | semidirect |
| 8. #4655 | C2 | semidirect |
| 9. #4654 | C2 | semidirect |
| 210. C3 | #2569 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#95 | 2 |
| #5212 | 2 |
| #5210 | 2 |
| C4×#217 | 2 |
| #4661 | 2 |
| #4660 | 2 |
| #4655 | 2 |
| #4654 | 2 |
| #2569 | 3 |