Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
352 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 352 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. #5730 | C2 | semidirect |
| 2. #5543 | C2 | semidirect |
| 3. C3×#476 | C2 | semidirect |
| 4. #5078 | C2 | semidirect |
| 6. #4871 | C2 | semidirect |
| 7. #4858 | C2 | semidirect |
| 8. #4842 | C2 | semidirect |
| 9. #4830 | C2 | semidirect |
| 10. #4763 | C2 | semidirect |
| 49. #476 | D3 | semidirect |
| 69. #213 | Q8 | semidirect |
| 233. C3 | #3380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5730 | 2 |
| #5543 | 2 |
| C3×#476 | 2 |
| #5078 | 2 |
| C4×#213 | 2 |
| #4871 | 2 |
| #4858 | 2 |
| #4842 | 2 |
| #4830 | 2 |
| #4763 | 2 |
| #4756 | 2 |
| #3380 | 3 |