Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#930 | C2 | semidirect |
| 2. C2×C3×C22⋊C8 | C2 | semidirect |
| 3. #5115 | C2 | semidirect |
| 4. #4736 | C2 | semidirect |
| 5. #4732 | C2 | semidirect |
| 9. C22×D12 | C22 | semidirect |
| 10. C22×C3×C8 | C22 | semidirect |
| 14. #930 | C22 | semidirect |
| 16. C2×C4⋊Dic3 | C22 | semidirect |
| 17. C2×D24 | C22 | semidirect |
| 18. C3×C22⋊C8 | C22 | semidirect |
| 19. #821 | C22 | semidirect |
| 20. #818 | C22 | semidirect |
| 25. C2×C22⋊C8 | D3 | semidirect |
| 51. C22×C8 | C2×D3 | semidirect |
| 60. C22⋊C8 | C2×D3 | semidirect |
| 63. C23×C3 | D8 | semidirect |
| 127. C23 | D24 | semidirect |
| 166. C3 | #3186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#930 | 2 |
| C2×C3×C22⋊C8 | 2 |
| #5115 | 2 |
| #4736 | 2 |
| #4732 | 2 |
| #3186 | 3 |