Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
454 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 108 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. #14545009 | C2 | semidirect |
| 2. #14543720 | C2 | semidirect |
| 3. #14543705 | C2 | semidirect |
| 52. C2×D68 | C16 | semidirect |
| 90. C22×D17 | C2×C16 | semidirect |
| 98. C2×C4×C17 | C2×C16 | semidirect |
| 188. C17 | #11465 | semidirect |
| 254. C2×C4 | #10587529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545009 | 2 |
| #14543720 | 2 |
| #14543705 | 2 |
| C2×C8×D68 | 2 |
| #11465 | 17 |