Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
456 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 88 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. #14544664 | C2 | semidirect |
| 2. #14544661 | C2 | semidirect |
| 4. #14543684 | C2 | semidirect |
| 20. #11762837 | C4 | semidirect |
| 21. #11762776 | C4 | semidirect |
| 23. #11762764 | C4 | semidirect |
| 24. C2×C17×#131 | C4 | semidirect |
| 187. C2×#131 | #595 | semidirect |
| 253. C17 | #8627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544664 | 2 |
| #14544661 | 2 |
| #14544199 | 2 |
| #14543684 | 2 |
| #14537476 | 2 |
| #8627 | 17 |