Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
318 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 318 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 |
|---|---|---|
| 14. #11763734 | C4 | semidirect |
| 15. #11763700 | C4 | semidirect |
| 21. #11762637 | C4 | semidirect |
| 22. #11762636 | C4 | semidirect |
| 23. #11762634 | C4 | semidirect |
| 24. C17×#366 | C4 | semidirect |
| 84. C16×C17 | C42 | semidirect |
| 85. #63214 | C42 | semidirect |
| 146. #366 | #595 | semidirect |
| 186. C17 | #12677 | semidirect |
| 217. 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×#11763700 | 2 |
| #14544599 | 2 |
| #14544591 | 2 |
| #14543858 | 2 |
| #14543855 | 2 |
| #14530569 | 2 |
| #12677 | 17 |