Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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. #5479 | C2 | semidirect |
| 2. #5477 | C2 | semidirect |
| 3. C2×C3×C4⋊C8 | C2 | semidirect |
| 4. #5115 | C2 | semidirect |
| 5. #5114 | C2 | semidirect |
| 6. #4850 | C2 | semidirect |
| 7. #4848 | C2 | semidirect |
| 8. #4847 | C2 | semidirect |
| 9. #4844 | C2 | semidirect |
| 10. #4843 | C2 | semidirect |
| 11. #4842 | C2 | semidirect |
| 54. C2×C4⋊C8 | D3 | semidirect |
| 276. C3 | #3247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5479 | 2 |
| #5477 | 2 |
| C2×C3×C4⋊C8 | 2 |
| #5115 | 2 |
| #5114 | 2 |
| #4850 | 2 |
| #4848 | 2 |
| #4847 | 2 |
| #4844 | 2 |
| #4843 | 2 |
| #4842 | 2 |
| #3247 | 3 |