Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
456 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 181 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. #4790 | C2 | semidirect |
| 9. #4789 | C2 | semidirect |
| 17. C2×#216 | C4 | semidirect |
| 193. C3 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5812 | 2 |
| C22×#216 | 2 |
| #5516 | 2 |
| C3×#419 | 2 |
| #5122 | 2 |
| #5120 | 2 |
| #4998 | 2 |
| #4790 | 2 |
| #4789 | 2 |
| #2950 | 3 |