Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
456 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 177 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. C2×#907 | C2 | semidirect |
| 3. C3×#430 | C2 | semidirect |
| 4. #5139 | C2 | semidirect |
| 5. #5122 | C2 | semidirect |
| 6. #4895 | C2 | semidirect |
| 7. #4894 | C2 | semidirect |
| 14. #909 | C4 | semidirect |
| 15. #908 | C4 | semidirect |
| 18. #907 | C22 | semidirect |
| 19. #907 | C22 | semidirect |
| 23. C3×#108 | C22 | semidirect |
| 24. #825 | C22 | semidirect |
| 25. #815 | C22 | semidirect |
| 26. C8×Dic3 | C22 | semidirect |
| 31. #430 | D3 | semidirect |
| 76. #108 | C2×D3 | semidirect |
| 174. C3 | #2955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5748 | 2 |
| C2×#907 | 2 |
| C3×#430 | 2 |
| #5139 | 2 |
| #5122 | 2 |
| #4895 | 2 |
| #4894 | 2 |
| #2955 | 3 |