Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
958 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 187 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. C2×#11763179 | C2 | semidirect |
| 2. C2×#11763168 | C2 | semidirect |
| 3. #14528107 | C2 | direct (N × H) |
| 4. C2×#11762551 | C2 | semidirect |
| 5. C2×#11762549 | C2 | semidirect |
| 9. #11763179 | C22 | semidirect |
| 11. #11763168 | C22 | semidirect |
| 17. #11762551 | C22 | semidirect |
| 18. #11762549 | C22 | semidirect |
| 172. C2×C17 | #1662 | semidirect |
| 213. C17 | C2×#1662 | semidirect |
| 294. C2 | #14528107 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763179 | 2 |
| C2×#11763168 | 2 |
| #14528107 | 2 |
| C2×#11762551 | 2 |
| C2×#11762549 | 2 |
| C2×C17×#562 | 2 |
| C2×#1662 | 17 |