Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
730 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14537807 | C2 | semidirect |
| 3. #14528773 | C2 | semidirect |
| 4. #14527452 | C2 | semidirect |
| 5. #14526686 | C2 | semidirect |
| 6. #14526685 | C2 | semidirect |
| 7. C17×#1545 | C2 | semidirect |
| 54. C17×C4⋊C8 | D4 | semidirect |
| 63. C4⋊#3622 | D4 | semidirect |
| 169. #1545 | D17 | semidirect |
| 253. C4⋊C8 | C22⋊D17 | semidirect |
| 261. C17 | #9397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537807 | 2 |
| #14533731 | 2 |
| #14528773 | 2 |
| #14527452 | 2 |
| #14526686 | 2 |
| #14526685 | 2 |
| C17×#1545 | 2 |
| #9397 | 17 |