Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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×#557 | C2 | semidirect |
| 3. #5093 | C2 | semidirect |
| 6. #5063 | C2 | semidirect |
| 7. #5031 | C2 | semidirect |
| 8. C4×#216 | C2 | semidirect |
| 11. Q8×C3⋊C8 | C2 | semidirect |
| 42. #557 | D3 | semidirect |
| 226. C3 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#557 | 2 |
| #5584 | 2 |
| #5093 | 2 |
| #5087 | 2 |
| #5068 | 2 |
| #5063 | 2 |
| #5031 | 2 |
| C4×#216 | 2 |
| #5028 | 2 |
| C4×#215 | 2 |
| Q8×C3⋊C8 | 2 |
| #3364 | 3 |