Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
708 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 126 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. #14544674 | C2 | semidirect |
| 2. C2×#11763675 | C2 | semidirect |
| 3. #14543605 | C2 | semidirect |
| 4. #14543601 | C2 | semidirect |
| 30. C2×#63252 | C8 | semidirect |
| 88. C2×D68 | C2×C8 | semidirect |
| 95. C2×Dic34 | C2×C8 | semidirect |
| 272. C17 | #7578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544674 | 2 |
| C2×#11763675 | 2 |
| #14543605 | 2 |
| #14543601 | 2 |
| #14531272 | 2 |
| #7578 | 17 |