Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
558 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 558 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. #14545009 | C2 | semidirect |
| 2. C2×#11763683 | C2 | semidirect |
| 3. #14543771 | C2 | semidirect |
| 4. #14543770 | C2 | semidirect |
| 8. #11763704 | C22 | semidirect |
| 11. #11763683 | C22 | semidirect |
| 12. C2×D8×D17 | C4 | semidirect |
| 16. #11763045 | C4 | semidirect |
| 20. #107×D17 | C4 | semidirect |
| 22. C17×#466 | C4 | semidirect |
| 31. C2×D8×C17 | C2×C4 | semidirect |
| 40. C2×D136 | C2×C4 | semidirect |
| 52. C17×#107 | C2×C4 | semidirect |
| 56. #10587489 | C2×C4 | semidirect |
| 200. #466 | #595 | semidirect |
| 215. D17 | #1347 | semidirect |
| 223. C2×D8 | C2×#595 | semidirect |
| 247. #107 | C2×#595 | semidirect |
| 252. C17 | C2×#1347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545009 | 2 |
| C2×#11763683 | 2 |
| #14543771 | 2 |
| #14543770 | 2 |
| D17×#466 | 2 |
| C2×#1347 | 17 |