Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
846 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 246 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×Dic36 | C2 | semidirect |
| 4. C2×#63431 | C2 | semidirect |
| 5. C2×C9×#97 | C2 | semidirect |
| 6. #10588396 | C2 | direct (N × H) |
| 18. C2×Dic36 | C22 | semidirect |
| 22. #63431 | C22 | semidirect |
| 23. C9×#97 | C22 | semidirect |
| 96. C2×#97 | D9 | semidirect |
| 146. #97 | C2×D9 | semidirect |
| 168. C2×C9 | #497 | semidirect |
| 206. C9 | C2×#497 | semidirect |
| 245. C2 | #10588396 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3664 | 2 |
| C22×Dic36 | 2 |
| C2×#63437 | 2 |
| C2×#63431 | 2 |
| C2×C9×#97 | 2 |
| #10588396 | 2 |
| C2×#4715 | 3 |