Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #5519 | C2 | semidirect |
| 3. C3×#428 | C2 | semidirect |
| 5. #5119 | C2 | semidirect |
| 7. C2×#808 | C2 | semidirect |
| 8. #4891 | C2 | semidirect |
| 9. #4877 | C2 | semidirect |
| 10. #4870 | C2 | semidirect |
| 11. #4854 | C2 | semidirect |
| 48. #428 | D3 | semidirect |
| 58. #235 | Q8 | semidirect |
| 241. C3 | #3084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5519 | 2 |
| #5504 | 2 |
| C3×#428 | 2 |
| #5133 | 2 |
| #5119 | 2 |
| #5002 | 2 |
| C2×#808 | 2 |
| #4891 | 2 |
| #4877 | 2 |
| #4870 | 2 |
| #4854 | 2 |
| #3084 | 3 |