Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1068 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 209 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×#379 | C2 |
| prime radical | C25×C3 | C22 |
| hypercenter | #379 | D3 |
| hypocenter | C3 | #2848 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#878 | C2 | semidirect |
| 5. #4950 | C2 | semidirect |
| 6. #4946 | C2 | semidirect |
| 7. #4942 | C2 | semidirect |
| 13. C22×Dic6 | C22 | semidirect |
| 18. C2×C4⋊Dic3 | C22 | semidirect |
| 19. C2×Dic3⋊C4 | C22 | semidirect |
| 20. C2×Dic3⋊C4 | C22 | semidirect |
| 22. C3⋊#95 | C22 | semidirect |
| 32. C24×C3 | Q8 | semidirect |
| 90. C24 | Dic6 | semidirect |
| 116. C22×C3 | C22⋊Q8 | semidirect |
| 156. C22 | #878 | semidirect |
| 166. C3 | #2848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic3 | 2 |
| C2×#878 | 2 |
| C3×#379 | 2 |
| #5247 | 2 |
| #4950 | 2 |
| #4946 | 2 |
| #4942 | 2 |
| #2848 | 3 |