Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
912 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 109 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. #14537810 | C2 | semidirect |
| 3. #14528769 | C2 | semidirect |
| 4. #14528715 | C2 | semidirect |
| 5. #14526652 | C2 | semidirect |
| 6. #14526651 | C2 | semidirect |
| 7. C17×#1786 | C2 | semidirect |
| 18. #11762723 | C4 | semidirect |
| 19. #11762717 | C4 | semidirect |
| 41. C22×C8×C17 | D4 | semidirect |
| 62. C22×#3622 | D4 | semidirect |
| 230. #1786 | D17 | semidirect |
| 322. C22×C8 | C22⋊D17 | semidirect |
| 356. C17 | #9472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537810 | 2 |
| #14532134 | 2 |
| #14528769 | 2 |
| #14528715 | 2 |
| #14526652 | 2 |
| #14526651 | 2 |
| C17×#1786 | 2 |
| #9472 | 17 |