Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
334 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 14. #11762584 | C4 | semidirect |
| 15. C4×#63214 | C4 | semidirect |
| 16. C4×C16×C17 | C4 | semidirect |
| 56. C16×C17 | C4⋊C4 | semidirect |
| 57. #63214 | C4⋊C4 | semidirect |
| 85. C4×C17 | #365 | semidirect |
| 102. C4×C16 | #595 | semidirect |
| 126. C17 | #12903 | semidirect |
| 148. C16 | C4⋊#595 | semidirect |
| 174. C4 | #11763734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763734 | 2 |
| #14544723 | 2 |
| #14544719 | 2 |
| C4×#10587469 | 2 |
| #12903 | 17 |