Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1328 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 291 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. #14543496 | C2 | semidirect |
| 2. #14537479 | C2 | semidirect |
| 3. #14529203 | C2 | semidirect |
| 4. #14529072 | C2 | semidirect |
| 5. #14528735 | C2 | semidirect |
| 6. #14528586 | C2 | semidirect |
| 12. C23×#3622 | C22 | semidirect |
| 15. #11762836 | C22 | semidirect |
| 18. #11762773 | C22 | semidirect |
| 19. #11762765 | C22 | semidirect |
| 20. #11762579 | C22 | semidirect |
| 45. C2×#63223 | D4 | semidirect |
| 51. C22×#3622 | D4 | semidirect |
| 206. C17 | #21483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14543496 | 2 |
| #14537479 | 2 |
| #14529203 | 2 |
| #14529072 | 2 |
| #14528735 | 2 |
| #14528586 | 2 |
| C17×#3025 | 2 |
| #21483 | 17 |