Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
908 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 203 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×#396 | C2 |
| prime radical | C24×D3 | C22 |
| hypercenter | #396 | D3 |
| hypocenter | C3 | C2×#396 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #396 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D3×C4⋊C4 | C2 | semidirect |
| 3. C3×#396 | C2 | semidirect |
| 4. #4994 | C2 | semidirect |
| 5. #4948 | C2 | semidirect |
| 6. #4676 | C2 | semidirect |
| 7. D3×#95 | C2 | semidirect |
| 12. C2×C3×C4⋊C4 | C22 | semidirect |
| 17. C2×C4⋊Dic3 | C22 | semidirect |
| 18. C2×Dic3⋊C4 | C22 | semidirect |
| 19. C2×Dic3⋊C4 | C22 | semidirect |
| 22. C3×#95 | C22 | semidirect |
| 23. C3⋊#95 | C22 | semidirect |
| 29. #396 | D3 | direct (N × H) |
| 62. C2×C4⋊C4 | C2×D3 | semidirect |
| 69. #95 | C2×D3 | semidirect |
| 170. D3 | #396 | direct (N × H) |
| 188. C3 | C2×#396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C4⋊C4 | 2 |
| C2×D3×C22⋊C4 | 2 |
| C3×#396 | 2 |
| #4994 | 2 |
| #4948 | 2 |
| #4676 | 2 |
| D3×#95 | 2 |
| C2×#396 | 3 |