Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1328 conjugacy classes of subgroups; only the 279 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 279 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 |
|---|---|---|
| 2. #14537476 | C2 | semidirect |
| 3. #14529202 | C2 | semidirect |
| 4. #14529070 | C2 | semidirect |
| 5. #14528735 | C2 | semidirect |
| 6. #14528584 | C2 | semidirect |
| 7. C17×#3573 | C2 | semidirect |
| 8. C22×C8×D17 | C22 | semidirect |
| 14. #11762837 | C22 | semidirect |
| 18. #11762772 | C22 | semidirect |
| 19. #11762764 | C22 | semidirect |
| 20. #11762580 | C22 | semidirect |
| 39. C2×M16×C17 | D4 | semidirect |
| 42. C22×C8×C17 | D4 | semidirect |
| 128. #3573 | D17 | semidirect |
| 184. C2×M16 | C22⋊D17 | semidirect |
| 190. C22×C8 | C22⋊D17 | semidirect |
| 206. C17 | #21483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538176 | 2 |
| #14537476 | 2 |
| #14529202 | 2 |
| #14529070 | 2 |
| #14528735 | 2 |
| #14528584 | 2 |
| C17×#3573 | 2 |
| #21483 | 17 |