Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
690 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 95 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. #14537812 | C2 | semidirect |
| 3. #14527498 | C2 | semidirect |
| 4. #14527124 | C2 | semidirect |
| 5. #14526641 | C2 | semidirect |
| 6. #14526639 | C2 | semidirect |
| 7. C17×#1555 | C2 | semidirect |
| 59. C17×C4⋊C8 | D4 | semidirect |
| 70. C4⋊#3622 | D4 | semidirect |
| 186. #1555 | D17 | semidirect |
| 282. C4⋊C8 | C22⋊D17 | semidirect |
| 294. C17 | #9457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537812 | 2 |
| #14533731 | 2 |
| #14527498 | 2 |
| #14527124 | 2 |
| #14526641 | 2 |
| #14526639 | 2 |
| C17×#1555 | 2 |
| #9457 | 17 |