Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
470 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 90 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. #14545752 | C2 | semidirect |
| 2. C2×#11763727 | C2 | semidirect |
| 3. #14545093 | C2 | semidirect |
| 4. #14544670 | C2 | semidirect |
| 5. #14543864 | C2 | semidirect |
| 6. #14543853 | C2 | semidirect |
| 25. #11763080 | C4 | semidirect |
| 26. #11763079 | C4 | semidirect |
| 29. #11763076 | C4 | semidirect |
| 32. C17×#472 | C4 | semidirect |
| 238. #472 | #595 | semidirect |
| 310. C17 | #13068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545752 | 2 |
| C2×#11763727 | 2 |
| #14545093 | 2 |
| #14544670 | 2 |
| #14543864 | 2 |
| #14543853 | 2 |
| D17×#472 | 2 |
| #13068 | 17 |