Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
376 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 8. #4799 | C2 | semidirect |
| 9. #4796 | C2 | semidirect |
| 10. #4793 | C2 | semidirect |
| 11. #4791 | C2 | semidirect |
| 57. C2×C3×Q8 | Q8 | semidirect |
| 155. C2×Q8 | Dic6 | semidirect |
| 254. C3 | #3078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic3 | 2 |
| #5517 | 2 |
| C3×#419 | 2 |
| #5225 | 2 |
| #5121 | 2 |
| #5118 | 2 |
| #4995 | 2 |
| #4799 | 2 |
| #4796 | 2 |
| #4793 | 2 |
| #4791 | 2 |
| #3078 | 3 |