Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
456 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 456 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×#11763725 | C2 | semidirect |
| 3. #14545099 | C2 | semidirect |
| 4. #14544672 | C2 | semidirect |
| 5. #14543861 | C2 | semidirect |
| 6. #14543850 | C2 | semidirect |
| 25. #11763085 | C4 | semidirect |
| 26. #11763084 | C4 | semidirect |
| 27. #11763076 | C4 | semidirect |
| 32. C17×#472 | C4 | semidirect |
| 233. #472 | #595 | semidirect |
| 306. C17 | #13070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545752 | 2 |
| C2×#11763725 | 2 |
| #14545099 | 2 |
| #14544672 | 2 |
| #14543861 | 2 |
| #14543850 | 2 |
| #14538502 | 2 |
| #13070 | 17 |