Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
854 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 203 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. C22×Dic136 | C2 | semidirect |
| 2. C22×#10587498 | C2 | semidirect |
| 3. C2×#11763192 | C2 | semidirect |
| 4. #14531042 | C2 | direct (N × H) |
| 5. C2×C16×Dic17 | C2 | semidirect |
| 11. C2×Dic136 | C22 | semidirect |
| 13. C2×#10587498 | C22 | semidirect |
| 16. #11763192 | C22 | semidirect |
| 18. C16×Dic17 | C22 | semidirect |
| 137. C2×C17 | #2249 | semidirect |
| 167. C17 | C2×#2249 | semidirect |
| 232. C2 | #14531042 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic136 | 2 |
| C22×#10587498 | 2 |
| C2×#11763192 | 2 |
| #14531042 | 2 |
| C2×C16×Dic17 | 2 |
| C22×C17×D16 | 2 |
| C2×#2249 | 17 |