Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1162 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1162 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. #14545899 | C2 | semidirect |
| 17. C22×Q8×C17 | C8 | semidirect |
| 20. C2×Q8×D17 | C8 | semidirect |
| 21. C2×Q8×D17 | C8 | semidirect |
| 25. C22×Dic34 | C8 | semidirect |
| 164. C22×Q8 | #3633 | semidirect |
| 184. C17 | #17352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14546027 | 2 |
| #14545899 | 2 |
| #14545896 | 2 |
| C2×#11763877 | 2 |
| #17352 | 17 |