Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
438 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 438 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 |
|---|---|---|
| 3. #14545001 | C2 | semidirect |
| 4. #14544598 | C2 | semidirect |
| 5. #14543860 | C2 | semidirect |
| 6. #14543850 | C2 | semidirect |
| 13. #11763726 | C4 | semidirect |
| 14. #11763725 | C4 | semidirect |
| 15. #11763722 | C4 | semidirect |
| 16. #11763721 | C4 | semidirect |
| 22. #11762932 | C4 | semidirect |
| 23. #11762931 | C4 | semidirect |
| 24. #11762930 | C4 | semidirect |
| 30. C17×#444 | C4 | semidirect |
| 97. Q16×C17 | C42 | semidirect |
| 99. D8×C17 | C42 | semidirect |
| 117. Dic68 | C42 | semidirect |
| 118. D136 | C42 | semidirect |
| 211. #444 | #595 | semidirect |
| 279. C17 | #12650 | semidirect |
| 296. Q16 | C4×#595 | semidirect |
| 303. D8 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#360 | 2 |
| #14545092 | 2 |
| #14545001 | 2 |
| #14544598 | 2 |
| #14543860 | 2 |
| #14543850 | 2 |
| D17×#444 | 2 |
| #12650 | 17 |