Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
732 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 198 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. C2×C9×#125 | C2 | semidirect |
| 3. #10588748 | C2 | direct (N × H) |
| 4. C2×#63369 | C2 | semidirect |
| 5. C2×#63362 | C2 | semidirect |
| 10. C9×#125 | C22 | semidirect |
| 17. #63369 | C22 | semidirect |
| 18. #63362 | C22 | semidirect |
| 69. C2×#125 | D9 | semidirect |
| 105. #125 | C2×D9 | semidirect |
| 126. C2×C9 | #490 | semidirect |
| 156. C9 | C2×#490 | semidirect |
| 188. C2 | #10588748 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#125 | 2 |
| C2×#63436 | 2 |
| #10588748 | 2 |
| C2×#63369 | 2 |
| C2×#63362 | 2 |
| C2×#5067 | 3 |