Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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×#556 | C2 | semidirect |
| 2. #5584 | C2 | semidirect |
| 3. #5092 | C2 | semidirect |
| 4. #5083 | C2 | semidirect |
| 6. #5054 | C2 | semidirect |
| 7. C4×#216 | C2 | semidirect |
| 8. #5028 | C2 | semidirect |
| 9. Q8×C3⋊C8 | C2 | semidirect |
| 10. #5019 | C2 | semidirect |
| 43. #556 | D3 | semidirect |
| 241. C3 | #3393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#556 | 2 |
| #5584 | 2 |
| #5092 | 2 |
| #5083 | 2 |
| #5059 | 2 |
| #5054 | 2 |
| C4×#216 | 2 |
| #5028 | 2 |
| Q8×C3⋊C8 | 2 |
| #5019 | 2 |
| C4×#213 | 2 |
| #3393 | 3 |