Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
897 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 897 conjugacy classes of subgroups — too many to draw. Only its 150 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×#3676 | C2 | semidirect |
| 3. #10588927 | C2 | semidirect |
| 4. C2×#63393 | C2 | semidirect |
| 5. #10588203 | C2 | semidirect |
| 8. C22×D4×C9 | C4 | semidirect |
| 14. C2×C9×C22⋊C4 | C4 | semidirect |
| 31. C24×C9 | C2×C4 | semidirect |
| 43. C22×C4×C9 | C2×C4 | semidirect |
| 44. C22×C4×C9 | C2×C4 | semidirect |
| 58. #3676 | D4 | semidirect |
| 170. C22×C9 | #99 | semidirect |
| 181. C22×D4 | Dic9 | semidirect |
| 192. C2×C22⋊C4 | Dic9 | semidirect |
| 247. C24 | C2×Dic9 | semidirect |
| 263. C22×C4 | C2×Dic9 | semidirect |
| 264. C22×C4 | C2×Dic9 | semidirect |
| 304. C9 | #1898 | semidirect |
| 372. C22 | #63393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#120 | 2 |
| C22×#3676 | 2 |
| #10588927 | 2 |
| C2×#63393 | 2 |
| #10588203 | 2 |
| #71670 | 3 |