Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
476 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 82 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. #14545560 | C2 | semidirect |
| 2. D17⋊#361 | C2 | semidirect |
| 3. #14545099 | C2 | semidirect |
| 4. #14544945 | C2 | semidirect |
| 5. #14543854 | C2 | semidirect |
| 6. #14543833 | C2 | semidirect |
| 24. C2×#10587471 | C4 | semidirect |
| 25. C2×#10587498 | C4 | semidirect |
| 26. C2×#10587497 | C4 | semidirect |
| 28. C2×C17×D16 | C4 | semidirect |
| 195. C2×D16 | #595 | semidirect |
| 259. C17 | #13036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545560 | 2 |
| D17⋊#361 | 2 |
| #14545099 | 2 |
| #14544945 | 2 |
| #14543854 | 2 |
| #14543833 | 2 |
| C2×#11763243 | 2 |
| #13036 | 17 |