Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #5748 | C2 | semidirect |
| 2. C2×#904 | C2 | semidirect |
| 3. C2×#901 | C2 | semidirect |
| 4. C2×C3×#108 | C2 | semidirect |
| 5. #5132 | C2 | semidirect |
| 6. #4898 | C2 | semidirect |
| 7. #4897 | C2 | semidirect |
| 8. #4896 | C2 | semidirect |
| 19. C2×Dic12 | C22 | semidirect |
| 25. C2×D24 | C22 | semidirect |
| 26. C2×#204 | C22 | semidirect |
| 33. C3×#108 | C22 | semidirect |
| 34. C3×#108 | C22 | semidirect |
| 35. #824 | C22 | semidirect |
| 36. #823 | C22 | semidirect |
| 43. C2×#108 | D3 | semidirect |
| 111. #108 | C2×D3 | semidirect |
| 112. #108 | C2×D3 | semidirect |
| 258. C3 | #3067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5748 | 2 |
| C2×#904 | 2 |
| C2×#901 | 2 |
| C2×C3×#108 | 2 |
| #5132 | 2 |
| #4898 | 2 |
| #4897 | 2 |
| #4896 | 2 |
| #3067 | 3 |