Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #5727 | C2 | semidirect |
| 2. D4×Dic6 | C2 | semidirect |
| 3. C3×#474 | C2 | semidirect |
| 4. #5078 | C2 | semidirect |
| 6. #4890 | C2 | semidirect |
| 7. #4874 | C2 | semidirect |
| 8. #4846 | C2 | semidirect |
| 9. #4830 | C2 | semidirect |
| 10. #4759 | C2 | semidirect |
| 49. #474 | D3 | semidirect |
| 73. #213 | Q8 | semidirect |
| 119. C3×D4 | C2×Q8 | semidirect |
| 132. D12 | C2×Q8 | semidirect |
| 138. Dic6 | D8 | semidirect |
| 141. C3⋊C8 | C2×Q8 | semidirect |
| 202. D4 | D3×Q8 | semidirect |
| 241. C3 | Q8×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5727 | 2 |
| D4×Dic6 | 2 |
| C3×#474 | 2 |
| #5078 | 2 |
| C4×#213 | 2 |
| #4890 | 2 |
| #4874 | 2 |
| #4846 | 2 |
| #4830 | 2 |
| #4759 | 2 |
| #4756 | 2 |
| Q8×D8 | 3 |