Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
510 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 3. C2×#11763699 | C2 | semidirect |
| 4. #14543824 | C2 | semidirect |
| 14. #11763704 | C4 | semidirect |
| 15. C22⋊#63216 | C4 | semidirect |
| 19. C22⋊#63214 | C4 | semidirect |
| 20. #11762588 | C4 | semidirect |
| 21. C17×C22⋊C16 | C4 | semidirect |
| 43. C2×#63216 | C2×C4 | semidirect |
| 50. C2×C16×C17 | C2×C4 | semidirect |
| 51. C2×#63214 | C2×C4 | semidirect |
| 144. C22×C17 | #347 | semidirect |
| 152. C2×D17 | #347 | semidirect |
| 177. C22⋊C16 | #595 | semidirect |
| 213. C2×C16 | C2×#595 | semidirect |
| 218. C17 | #12605 | semidirect |
| 312. C22 | #11763699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587532 | 2 |
| #14545012 | 2 |
| C2×#11763699 | 2 |
| #14543824 | 2 |
| #14530393 | 2 |
| #12605 | 17 |