Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 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. #14539522 | C2 | semidirect |
| 2. #14530998 | C2 | semidirect |
| 3. #14530955 | C2 | semidirect |
| 4. #14530860 | C2 | semidirect |
| 5. #14530730 | C2 | semidirect |
| 6. #14530682 | C2 | semidirect |
| 7. #14530596 | C2 | semidirect |
| 8. C17×#2956 | C2 | semidirect |
| 11. #11763207 | C22 | semidirect |
| 12. #11763186 | C22 | semidirect |
| 17. #11762922 | C22 | semidirect |
| 18. #11762633 | C22 | semidirect |
| 19. #11762630 | C22 | semidirect |
| 20. #11762621 | C22 | semidirect |
| 23. #11762587 | C22 | semidirect |
| 89. Q16×C17 | #41 | semidirect |
| 93. D8×C17 | #41 | semidirect |
| 151. #2956 | D17 | semidirect |
| 240. C17 | #33688 | semidirect |
| 259. Q16 | #63252 | semidirect |
| 265. D8 | #63252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539522 | 2 |
| #14530998 | 2 |
| #14530955 | 2 |
| #14530860 | 2 |
| #14530730 | 2 |
| #14530682 | 2 |
| #14530596 | 2 |
| C17×#2956 | 2 |
| #33688 | 17 |