Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
420 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 118 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. C2×#11763700 | C2 | semidirect |
| 4. #14543824 | C2 | semidirect |
| 7. C2×#10587530 | C4 | semidirect |
| 10. C22×#63216 | C4 | semidirect |
| 18. C22⋊#63214 | C4 | semidirect |
| 19. #11762588 | C4 | semidirect |
| 20. C17×C22⋊C16 | C4 | semidirect |
| 78. #63216 | C22⋊C4 | semidirect |
| 117. C22×C17 | #347 | semidirect |
| 144. C22⋊C16 | #595 | semidirect |
| 180. C17 | #12616 | semidirect |
| 251. C22 | #11763700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587530 | 2 |
| C2×#11763700 | 2 |
| #14544520 | 2 |
| #14543824 | 2 |
| #14530393 | 2 |
| #12616 | 17 |