Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×Q8×Dic3 | C2 | semidirect |
| 3. C3×#451 | C2 | semidirect |
| 5. #5185 | C2 | semidirect |
| 6. #5184 | C2 | semidirect |
| 7. #5044 | C2 | semidirect |
| 8. #4817 | C2 | semidirect |
| 9. #4799 | C2 | semidirect |
| 11. #4719 | C2 | semidirect |
| 50. #451 | D3 | semidirect |
| 257. C3 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic3 | 2 |
| #5624 | 2 |
| C3×#451 | 2 |
| #5227 | 2 |
| #5185 | 2 |
| #5184 | 2 |
| #5044 | 2 |
| #4817 | 2 |
| #4799 | 2 |
| #4735 | 2 |
| #4719 | 2 |
| #3117 | 3 |