Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 85 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. #14539787 | C2 | semidirect |
| 2. #14539158 | C2 | semidirect |
| 3. #14527498 | C2 | semidirect |
| 4. #14527382 | C2 | semidirect |
| 5. #14527295 | C2 | semidirect |
| 6. #14526677 | C2 | semidirect |
| 59. #10587555 | D4 | semidirect |
| 60. #10587555 | D4 | semidirect |
| 72. C4⋊#3622 | D4 | semidirect |
| 75. #10587474 | D4 | semidirect |
| 277. C17 | #10096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539787 | 2 |
| #14539158 | 2 |
| #14527498 | 2 |
| #14527382 | 2 |
| #14527295 | 2 |
| #14526677 | 2 |
| C17×#2657 | 2 |
| #10096 | 17 |