Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1258 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 159 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. C22×#3774 | C2 | semidirect |
| 2. C2×#63914 | C2 | semidirect |
| 3. C2×C4×#622 | C2 | semidirect |
| 4. #10593418 | C2 | direct (N × H) |
| 10. C2×#3774 | C22 | semidirect |
| 13. #63914 | C22 | semidirect |
| 14. C4×#622 | C22 | semidirect |
| 27. C2×#622 | D4 | semidirect |
| 45. C2×C32×C4 | D8 | semidirect |
| 47. C2×C3⋊Dic3 | D8 | semidirect |
| 56. #622 | C2×D4 | semidirect |
| 85. C32×C4 | C2×D8 | semidirect |
| 87. C3⋊Dic3 | C2×D8 | semidirect |
| 120. C2×C32 | #493 | semidirect |
| 157. C32 | C2×#493 | semidirect |
| 172. C2×C4 | #3774 | semidirect |
| 192. C4 | C2×#3774 | semidirect |
| 195. C2 | #10593418 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3774 | 2 |
| C2×#63914 | 2 |
| C2×C4×#622 | 2 |
| #10593418 | 2 |
| C2×#493 | 9 |