Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. #5543 | C2 | semidirect |
| 2. D4×Dic6 | C2 | semidirect |
| 5. #5008 | C2 | semidirect |
| 6. #5007 | C2 | semidirect |
| 7. #4876 | C2 | semidirect |
| 8. #4763 | C2 | semidirect |
| 9. #4761 | C2 | semidirect |
| 10. #4680 | C2 | semidirect |
| 11. #4679 | C2 | semidirect |
| 64. C3×D8 | Q8 | semidirect |
| 119. C3×D4 | C2×Q8 | semidirect |
| 138. C3×C8 | C2×Q8 | semidirect |
| 151. D8 | Dic6 | semidirect |
| 198. D4 | C2×Dic6 | semidirect |
| 214. C8 | C2×Dic6 | semidirect |
| 237. C3 | #3384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5543 | 2 |
| D4×Dic6 | 2 |
| C3×C4×D8 | 2 |
| #5152 | 2 |
| #5008 | 2 |
| #5007 | 2 |
| #4876 | 2 |
| #4763 | 2 |
| #4761 | 2 |
| #4680 | 2 |
| #4679 | 2 |
| #3384 | 3 |