Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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×#461 | C2 | semidirect |
| 5. #5164 | C2 | semidirect |
| 6. #5083 | C2 | semidirect |
| 7. #5007 | C2 | semidirect |
| 8. #4846 | C2 | semidirect |
| 9. #4835 | C2 | semidirect |
| 10. #4817 | C2 | semidirect |
| 11. #4811 | C2 | semidirect |
| 16. C3×C4⋊Q8 | C22 | semidirect |
| 19. Q8×Dic3 | C22 | semidirect |
| 33. #869 | C22 | semidirect |
| 34. C3×C4⋊C8 | C22 | semidirect |
| 35. C3×#103 | C22 | semidirect |
| 36. #835 | C22 | semidirect |
| 40. #818 | C22 | semidirect |
| 41. #815 | C22 | semidirect |
| 42. #807 | C22 | semidirect |
| 43. C4⋊(C3⋊C8) | C22 | semidirect |
| 50. #461 | D3 | semidirect |
| 100. C4⋊Q8 | C2×D3 | semidirect |
| 119. C4⋊C8 | C2×D3 | semidirect |
| 121. #103 | C2×D3 | semidirect |
| 286. C3 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| C4×D3×D4 | 2 |
| C3×#461 | 2 |
| #5169 | 2 |
| #5164 | 2 |
| #5083 | 2 |
| #5007 | 2 |
| #4846 | 2 |
| #4835 | 2 |
| #4817 | 2 |
| #4811 | 2 |
| #3110 | 3 |