Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
334 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 334 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 |
|---|---|---|
| 17. #11762585 | C4 | semidirect |
| 18. C16×Dic17 | C4 | semidirect |
| 19. C17×#346 | C4 | semidirect |
| 65. C16×C17 | C4⋊C4 | semidirect |
| 66. #63214 | C4⋊C4 | semidirect |
| 99. Dic17 | #365 | semidirect |
| 114. #346 | #595 | semidirect |
| 142. C17 | #12903 | semidirect |
| 167. C16 | C4⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763734 | 2 |
| C2×#11763733 | 2 |
| #14544724 | 2 |
| #14544719 | 2 |
| #14530377 | 2 |
| #12903 | 17 |