Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
458 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 458 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 |
|---|---|---|
| 1. C3×#519 | C2 | semidirect |
| 2. C22×#216 | C2 | semidirect |
| 5. #5031 | C2 | semidirect |
| 6. #5028 | C2 | semidirect |
| 7. #5004 | C2 | semidirect |
| 9. #4999 | C2 | semidirect |
| 37. #519 | D3 | semidirect |
| 218. C3 | #3044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#519 | 2 |
| C22×#216 | 2 |
| C2×#942 | 2 |
| #5526 | 2 |
| #5031 | 2 |
| #5028 | 2 |
| #5004 | 2 |
| #5002 | 2 |
| #4999 | 2 |
| #3044 | 3 |