Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
622 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 83 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. #14539773 | C2 | semidirect |
| 2. #14539702 | C2 | semidirect |
| 3. C2×#11763196 | C2 | semidirect |
| 4. #14527396 | C2 | semidirect |
| 5. #14527137 | C2 | semidirect |
| 6. #14526682 | C2 | semidirect |
| 7. C17×#1555 | C2 | semidirect |
| 175. #1555 | D17 | semidirect |
| 278. C17 | #10128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539773 | 2 |
| #14539702 | 2 |
| C2×#11763196 | 2 |
| #14527396 | 2 |
| #14527137 | 2 |
| #14526682 | 2 |
| C17×#1555 | 2 |
| #10128 | 17 |