Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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. #5713 | C2 | semidirect |
| 2. #5585 | C2 | semidirect |
| 3. C3×#460 | C2 | semidirect |
| 4. #5168 | C2 | semidirect |
| 5. #5165 | C2 | semidirect |
| 7. C4×#216 | C2 | semidirect |
| 8. #4848 | C2 | semidirect |
| 9. #4830 | C2 | semidirect |
| 10. #4787 | C2 | semidirect |
| 11. #4756 | C2 | semidirect |
| 49. #460 | D3 | semidirect |
| 249. C3 | #3396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5713 | 2 |
| #5585 | 2 |
| C3×#460 | 2 |
| #5168 | 2 |
| #5165 | 2 |
| #5073 | 2 |
| C4×#216 | 2 |
| #4848 | 2 |
| #4830 | 2 |
| #4787 | 2 |
| #4756 | 2 |
| #3396 | 3 |