Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
272 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 81 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. #4932 | C2 | semidirect |
| 3. #4926 | C2 | semidirect |
| 4. #4537 | C2 | semidirect |
| 7. C3×C4⋊Q8 | C4 | semidirect |
| 8. C3×#127 | C4 | semidirect |
| 13. C3×C4×D4 | C4 | semidirect |
| 47. C4⋊Q8 | Dic3 | semidirect |
| 48. #127 | Dic3 | semidirect |
| 53. C4×D4 | Dic3 | semidirect |
| 161. C3 | #1505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#532 | 2 |
| #4932 | 2 |
| #4926 | 2 |
| #4537 | 2 |
| #1505 | 3 |