Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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. #5812 | C2 | semidirect |
| 3. C3×#419 | C2 | semidirect |
| 6. #4559 | C2 | semidirect |
| 7. #4531 | C2 | semidirect |
| 15. C2×#216 | C4 | semidirect |
| 18. C2×#215 | C4 | semidirect |
| 29. #419 | D3 | semidirect |
| 213. C3 | #1905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5812 | 2 |
| C2×#942 | 2 |
| C3×#419 | 2 |
| #5139 | 2 |
| #5006 | 2 |
| #4559 | 2 |
| #4531 | 2 |
| #1905 | 3 |