Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1170 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 2. #14528546 | C2 | semidirect |
| 3. C2×#11762548 | C2 | semidirect |
| 4. C17×#1749 | C2 | semidirect |
| 15. C2×#10587474 | C22 | semidirect |
| 20. C2×C17×#97 | C22 | semidirect |
| 176. #1749 | D17 | semidirect |
| 184. C22×C17 | #329 | semidirect |
| 220. C2×#97 | C2×D17 | semidirect |
| 271. C17 | #8334 | semidirect |
| 399. C22 | #11762548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587561 | 2 |
| #14528546 | 2 |
| C2×#11762548 | 2 |
| C17×#1749 | 2 |
| #8334 | 17 |