Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1036 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 253 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic6 | C2 | semidirect |
| 4. C2×C3×#95 | C2 | semidirect |
| 5. C2×C3⋊#95 | C2 | semidirect |
| 6. #4673 | C2 | direct (N × H) |
| 15. C22×Dic6 | C22 | semidirect |
| 20. C3×#95 | C22 | semidirect |
| 21. C3⋊#95 | C22 | semidirect |
| 27. C2×#95 | D3 | semidirect |
| 33. C23×D3 | Q8 | semidirect |
| 67. #95 | C2×D3 | semidirect |
| 83. C22×D3 | C2×Q8 | semidirect |
| 176. C2×C3 | #393 | semidirect |
| 203. C3 | C2×#393 | semidirect |
| 205. C2 | #4673 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic6 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C2×C3×#95 | 2 |
| C2×C3⋊#95 | 2 |
| #4673 | 2 |
| C2×#393 | 3 |