Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 55. C2×C3×Q8 | Q8 | semidirect |
| 141. C2×Q8 | Dic6 | semidirect |
| 228. C3 | #3082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5812 | 2 |
| #5500 | 2 |
| C2×C3×#103 | 2 |
| #5225 | 2 |
| #5106 | 2 |
| #5102 | 2 |
| #4964 | 2 |
| #4799 | 2 |
| #4796 | 2 |
| #4793 | 2 |
| #4791 | 2 |
| #3082 | 3 |