Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1026 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 274 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. #10593795 | C2 | direct (N × H) |
| 4. C2×C4⋊#622 | C2 | semidirect |
| 5. C2×C4×#622 | C2 | semidirect |
| 17. C4⋊#622 | C22 | semidirect |
| 18. C4×#622 | C22 | semidirect |
| 21. C22×C32×C4 | C8 | semidirect |
| 59. C2×C32×C4 | C2×C8 | semidirect |
| 151. C2×C32 | #431 | semidirect |
| 165. C22×C4 | #622 | semidirect |
| 192. C32 | C2×#431 | semidirect |
| 212. C2×C4 | C2×#622 | semidirect |
| 238. C2 | #10593795 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C3⋊Dic3 | 2 |
| C2×C22⋊#622 | 2 |
| #10593795 | 2 |
| C2×C4⋊#622 | 2 |
| C2×C4×#622 | 2 |
| C2×#431 | 9 |