Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. C3×#462 | C2 | semidirect |
| 4. #5188 | C2 | semidirect |
| 5. #5186 | C2 | semidirect |
| 6. #5079 | C2 | semidirect |
| 7. C4×#216 | C2 | semidirect |
| 8. #4850 | C2 | semidirect |
| 10. #4811 | C2 | semidirect |
| 11. D3×#103 | C2 | semidirect |
| 48. #462 | D3 | semidirect |
| 132. D12 | Q16 | semidirect |
| 240. C3 | #3299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5727 | 2 |
| #5579 | 2 |
| C3×#462 | 2 |
| #5188 | 2 |
| #5186 | 2 |
| #5079 | 2 |
| C4×#216 | 2 |
| #4850 | 2 |
| #4834 | 2 |
| #4811 | 2 |
| D3×#103 | 2 |
| #3299 | 3 |