Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5021 | C2 | semidirect |
| 7. #4884 | C2 | semidirect |
| 8. #4813 | C2 | semidirect |
| 9. D3×#103 | C2 | semidirect |
| 11. #4681 | C2 | semidirect |
| 50. C4×Q16 | D3 | semidirect |
| 132. D12 | Q16 | semidirect |
| 240. C3 | #3299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5579 | 2 |
| Q8×D12 | 2 |
| C3×C4×Q16 | 2 |
| #5186 | 2 |
| #5031 | 2 |
| #5021 | 2 |
| #4884 | 2 |
| #4813 | 2 |
| D3×#103 | 2 |
| C8×D12 | 2 |
| #4681 | 2 |
| #3299 | 3 |