Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 2. C2×#888 | C2 | semidirect |
| 3. C3×#428 | C2 | semidirect |
| 5. #5118 | C2 | semidirect |
| 6. #4995 | C2 | semidirect |
| 8. #4890 | C2 | semidirect |
| 9. #4875 | C2 | semidirect |
| 10. #4870 | C2 | semidirect |
| 11. #4854 | C2 | semidirect |
| 51. #428 | D3 | semidirect |
| 62. #235 | Q8 | semidirect |
| 147. D12 | C2×Q8 | semidirect |
| 154. Dic6 | C2×Q8 | semidirect |
| 271. C3 | #3079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5522 | 2 |
| C2×#888 | 2 |
| C3×#428 | 2 |
| #5133 | 2 |
| #5118 | 2 |
| #4995 | 2 |
| #4966 | 2 |
| #4890 | 2 |
| #4875 | 2 |
| #4870 | 2 |
| #4854 | 2 |
| #3079 | 3 |