Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
430 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 98 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. #14545123 | C2 | semidirect |
| 3. #14544719 | C2 | semidirect |
| 4. #14543850 | C2 | semidirect |
| 16. #11762927 | C4 | semidirect |
| 17. #11762926 | C4 | semidirect |
| 18. #11762925 | C4 | semidirect |
| 24. C17×#443 | C4 | semidirect |
| 83. Q16×C17 | C4⋊C4 | semidirect |
| 85. D8×C17 | C4⋊C4 | semidirect |
| 103. Dic68 | C4⋊C4 | semidirect |
| 104. D136 | C4⋊C4 | semidirect |
| 189. #443 | #595 | semidirect |
| 248. C17 | #12823 | semidirect |
| 264. Q16 | C4⋊#595 | semidirect |
| 271. D8 | C4⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545123 | 2 |
| D17⋊#360 | 2 |
| #14544719 | 2 |
| #14543850 | 2 |
| D17×#443 | 2 |
| #12823 | 17 |