Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1238 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1238 conjugacy classes of subgroups — too many to draw. Only its 291 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. #14546027 | C2 | semidirect |
| 2. #14545898 | C2 | semidirect |
| 3. #14545896 | C2 | semidirect |
| 18. C2×#41×C17 | C8 | semidirect |
| 21. C2×#63256 | C8 | semidirect |
| 23. C2×#63254 | C8 | semidirect |
| 25. C2×#63252 | C8 | semidirect |
| 164. C2×#41 | #3633 | semidirect |
| 186. C17 | #17353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14546027 | 2 |
| #14545898 | 2 |
| #14545896 | 2 |
| C2×#11763878 | 2 |
| #17353 | 17 |