Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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. C3×C4×Q16 | C2 | semidirect |
| 3. #5188 | C2 | semidirect |
| 4. #5188 | C2 | semidirect |
| 5. #5022 | C2 | semidirect |
| 6. #4880 | C2 | semidirect |
| 7. D3×#107 | C2 | semidirect |
| 8. #4815 | C2 | semidirect |
| 9. #4805 | C2 | semidirect |
| 11. #4683 | C2 | semidirect |
| 47. C4×Q16 | D3 | semidirect |
| 223. C3 | #3336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5581 | 2 |
| C3×C4×Q16 | 2 |
| #5188 | 2 |
| #5022 | 2 |
| #4880 | 2 |
| D3×#107 | 2 |
| #4815 | 2 |
| #4805 | 2 |
| C8×D12 | 2 |
| #4683 | 2 |
| #3336 | 3 |