Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1134 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 328 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. C9×#568 | C2 | semidirect |
| 3. #10589921 | C2 | semidirect |
| 4. #10588814 | C2 | semidirect |
| 5. C2×#63383 | C2 | semidirect |
| 15. C2×C9×M16 | C22 | semidirect |
| 17. C2×#3667 | C22 | semidirect |
| 18. #63383 | C22 | semidirect |
| 19. #63382 | C22 | semidirect |
| 84. #568 | D9 | semidirect |
| 130. C2×M16 | C2×D9 | semidirect |
| 190. C9 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63715 | 2 |
| C9×#568 | 2 |
| #10589921 | 2 |
| #10588814 | 2 |
| C2×#63383 | 2 |
| #83813 | 3 |