Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 5. #5022 | C2 | semidirect |
| 6. #5022 | C2 | semidirect |
| 7. #5021 | C2 | semidirect |
| 8. #5020 | 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 |
|---|---|
| C3×#519 | 2 |
| #5519 | 2 |
| #5225 | 2 |
| C2×#835 | 2 |
| #5022 | 2 |
| #5021 | 2 |
| #5020 | 2 |
| #4999 | 2 |
| #4998 | 2 |
| #4995 | 2 |
| #3082 | 3 |