Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
846 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 214 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. C22×#3674 | C2 | semidirect |
| 4. C2×#63431 | C2 | semidirect |
| 5. #10588737 | C2 | direct (N × H) |
| 6. C2×#63362 | C2 | semidirect |
| 16. C2×#3674 | C22 | semidirect |
| 22. #63431 | C22 | semidirect |
| 23. #63362 | C22 | semidirect |
| 169. C2×C9 | #497 | semidirect |
| 206. C9 | C2×#497 | semidirect |
| 245. C2 | #10588737 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#124 | 2 |
| C22×#3674 | 2 |
| C22×#3672 | 2 |
| C2×#63431 | 2 |
| #10588737 | 2 |
| C2×#63362 | 2 |
| C2×#5060 | 3 |