Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
486 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 148 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×#11763696 | C2 | semidirect |
| 4. #14543821 | C2 | semidirect |
| 7. C2×#10587529 | 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 | #346 | semidirect |
| 122. C2×D17 | #346 | semidirect |
| 144. C22⋊C16 | #595 | semidirect |
| 180. C17 | #12611 | semidirect |
| 251. C22 | #11763696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587529 | 2 |
| C2×#11763696 | 2 |
| C8×C22⋊#595 | 2 |
| #14543821 | 2 |
| D17×C22⋊C16 | 2 |
| #12611 | 17 |