Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
4070 conjugacy classes of subgroups; only the 427 normal subgroups are shown.
This group has 4070 conjugacy classes of subgroups — too many to draw. Only its 427 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. C2×C22⋊C8×D17 | C2 | semidirect |
| 3. #14528696 | C2 | semidirect |
| 4. #14528695 | C2 | semidirect |
| 5. C17×#1780 | C2 | semidirect |
| 14. C2×C22⋊#3622 | C22 | semidirect |
| 15. C2×#10587491 | C22 | semidirect |
| 18. C2×C17×C22⋊C8 | C22 | semidirect |
| 126. #1780 | D17 | direct (N × H) |
| 154. C2×C22⋊C8 | C2×D17 | semidirect |
| 159. D17 | #1780 | direct (N × H) |
| 190. C17 | C2×#1780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41×D17 | 2 |
| C2×C22⋊C8×D17 | 2 |
| #14528696 | 2 |
| #14528695 | 2 |
| C17×#1780 | 2 |
| C2×#1780 | 17 |