Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
734 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 99 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. #14538785 | C2 | semidirect |
| 2. #14538784 | C2 | semidirect |
| 3. #14532063 | C2 | semidirect |
| 4. #14529615 | C2 | semidirect |
| 5. #14527208 | C2 | semidirect |
| 6. #14526612 | C2 | semidirect |
| 7. C17×#1486 | C2 | semidirect |
| 60. #10587560 | D4 | semidirect |
| 67. #10587555 | D4 | semidirect |
| 72. C4×C8×C17 | D4 | semidirect |
| 84. C4×#3622 | D4 | semidirect |
| 142. C4×Dic17 | D8 | semidirect |
| 206. #1486 | D17 | semidirect |
| 317. C4×C8 | C22⋊D17 | semidirect |
| 320. C17 | #10012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538785 | 2 |
| #14538784 | 2 |
| #14532063 | 2 |
| #14529615 | 2 |
| #14527208 | 2 |
| #14526612 | 2 |
| C17×#1486 | 2 |
| #10012 | 17 |