Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. #5728 | C2 | semidirect |
| 3. C3×#489 | C2 | semidirect |
| 4. #5089 | C2 | semidirect |
| 5. #5055 | C2 | semidirect |
| 6. #4802 | C2 | semidirect |
| 7. #4800 | C2 | semidirect |
| 9. #4768 | C2 | semidirect |
| 10. #4714 | C2 | semidirect |
| 11. #4707 | C2 | semidirect |
| 15. C3×C4⋊Q8 | C22 | semidirect |
| 24. #890 | C22 | semidirect |
| 32. #869 | C22 | semidirect |
| 33. C3×#103 | C22 | semidirect |
| 35. C3×#97 | C22 | semidirect |
| 36. #835 | C22 | semidirect |
| 39. #816 | C22 | semidirect |
| 40. C8×Dic3 | C22 | semidirect |
| 41. #810 | C22 | semidirect |
| 43. #803 | C22 | semidirect |
| 49. #489 | D3 | semidirect |
| 97. C4⋊Q8 | C2×D3 | semidirect |
| 116. #103 | C2×D3 | semidirect |
| 122. #97 | C2×D3 | semidirect |
| 270. C3 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| D3×#124 | 2 |
| C3×#489 | 2 |
| #5089 | 2 |
| #5055 | 2 |
| #4802 | 2 |
| #4800 | 2 |
| #4770 | 2 |
| #4768 | 2 |
| #4714 | 2 |
| #4707 | 2 |
| #3140 | 3 |