Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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. D4×Dic6 | C2 | semidirect |
| 3. #4848 | C2 | semidirect |
| 4. #4694 | C2 | semidirect |
| 5. C3×D4⋊C8 | C2 | semidirect |
| 6. #4482 | C2 | semidirect |
| 7. #4456 | C2 | semidirect |
| 32. D4⋊C8 | D3 | semidirect |
| 79. C3×D4 | SD16 | semidirect |
| 99. Dic6 | D8 | semidirect |
| 158. D4 | #204 | semidirect |
| 193. C3 | #1627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic6 | 2 |
| #5015 | 2 |
| #4848 | 2 |
| #4694 | 2 |
| C3×D4⋊C8 | 2 |
| #4482 | 2 |
| #4456 | 2 |
| #1627 | 3 |