Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. C3×C4×Q16 | C2 | semidirect |
| 4. #5186 | C2 | semidirect |
| 5. #5031 | C2 | semidirect |
| 6. #5020 | C2 | semidirect |
| 7. #4888 | C2 | semidirect |
| 8. #4816 | C2 | semidirect |
| 9. #4802 | C2 | semidirect |
| 11. #4681 | C2 | semidirect |
| 50. C4×Q16 | D3 | semidirect |
| 238. C3 | #3328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5584 | 2 |
| Q8×D12 | 2 |
| C3×C4×Q16 | 2 |
| #5186 | 2 |
| #5031 | 2 |
| #5020 | 2 |
| #4888 | 2 |
| #4816 | 2 |
| #4802 | 2 |
| #4688 | 2 |
| #4681 | 2 |
| #3328 | 3 |