Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1154 conjugacy classes of subgroups; only the 322 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 322 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 |
|---|---|---|
| 3. C2×#63777 | C2 | semidirect |
| 4. C2×C4×#622 | C2 | semidirect |
| 5. C4×#3788 | C2 | direct (N × H) |
| 10. C2×#3788 | C4 | direct (N × H) |
| 18. #63777 | C22 | semidirect |
| 19. C4×#622 | C22 | semidirect |
| 35. C2×#622 | C2×C4 | semidirect |
| 37. #3788 | C2×C4 | direct (N × H) |
| 61. C2×C32×C4 | M16 | semidirect |
| 66. C2×C3⋊Dic3 | M16 | semidirect |
| 76. #622 | C22×C4 | semidirect |
| 112. C32×C4 | C2×M16 | semidirect |
| 115. C3⋊Dic3 | C2×M16 | semidirect |
| 153. C2×C32 | C4×M16 | semidirect |
| 196. C32 | C2×C4×M16 | semidirect |
| 214. C2×C4 | #3788 | direct (N × H) |
| 238. C4 | C2×#3788 | direct (N × H) |
| 242. C2 | C4×#3788 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3788 | 2 |
| C2×C42×C3⋊D3 | 2 |
| C2×#63777 | 2 |
| C2×C4×#622 | 2 |
| C4×#3788 | 2 |
| C2×C4×M16 | 9 |