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 |
|---|---|---|
| 2. C2×#63432 | C2 | semidirect |
| 3. C2×C9×#97 | C2 | semidirect |
| 4. C2×#63380 | C2 | semidirect |
| 5. #10588394 | C2 | direct (N × H) |
| 16. #63432 | C22 | semidirect |
| 17. C9×#97 | C22 | semidirect |
| 18. #63380 | C22 | semidirect |
| 72. C2×#97 | D9 | semidirect |
| 110. #97 | C2×D9 | semidirect |
| 126. C2×C9 | #490 | semidirect |
| 156. C9 | C2×#490 | semidirect |
| 188. C2 | #10588394 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63436 | 2 |
| C2×#63432 | 2 |
| C2×C9×#97 | 2 |
| C2×#63380 | 2 |
| #10588394 | 2 |
| C2×#4713 | 3 |