Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #5519 | C2 | semidirect |
| 3. C3×#424 | C2 | semidirect |
| 5. #5121 | C2 | semidirect |
| 7. C2×#817 | C2 | semidirect |
| 8. #4851 | C2 | semidirect |
| 9. #4847 | C2 | semidirect |
| 10. #4842 | C2 | semidirect |
| 11. #4829 | C2 | semidirect |
| 50. #424 | 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 |
|---|---|
| #5523 | 2 |
| #5519 | 2 |
| C3×#424 | 2 |
| #5133 | 2 |
| #5121 | 2 |
| #5113 | 2 |
| C2×#817 | 2 |
| #4851 | 2 |
| #4847 | 2 |
| #4842 | 2 |
| #4829 | 2 |
| #3084 | 3 |