Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
396 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×#11763734 | C2 | semidirect |
| 4. #14543849 | C2 | semidirect |
| 15. C2×#10587469 | C4 | semidirect |
| 16. C2×#10587469 | C4 | semidirect |
| 19. C22×#63214 | C4 | semidirect |
| 20. C22×C16×C17 | C4 | semidirect |
| 80. C16×C17 | C22⋊C4 | semidirect |
| 82. #63214 | C22⋊C4 | semidirect |
| 119. C22×C17 | #365 | semidirect |
| 141. C22×C16 | #595 | semidirect |
| 184. C17 | #12831 | semidirect |
| 217. C16 | C22⋊#595 | semidirect |
| 255. C22 | #11763734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763734 | 2 |
| #14544663 | 2 |
| #14544660 | 2 |
| #14543849 | 2 |
| C22×#10587469 | 2 |
| #12831 | 17 |