Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
682 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 682 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 |
|---|---|---|
| 3. #14530889 | C2 | direct (N × H) |
| 4. C2×#11762637 | C2 | semidirect |
| 5. C2×#11762613 | C2 | semidirect |
| 6. C22×C17×Q32 | C2 | semidirect |
| 16. #11762637 | C22 | semidirect |
| 17. #11762613 | C22 | semidirect |
| 20. C2×C17×Q32 | C22 | semidirect |
| 104. C22×Q32 | D17 | semidirect |
| 126. C2×Q32 | C2×D17 | semidirect |
| 137. C2×C17 | #2219 | semidirect |
| 167. C17 | C2×#2219 | semidirect |
| 236. C2 | #14530889 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587469 | 2 |
| C2×#11763047 | 2 |
| #14530889 | 2 |
| C2×#11762637 | 2 |
| C2×#11762613 | 2 |
| C22×C17×Q32 | 2 |
| C2×#2219 | 17 |