Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
470 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 155 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×#11763241 | C2 | semidirect |
| 2. #14531091 | C2 | direct (N × H) |
| 3. C2×#11762649 | C2 | semidirect |
| 4. C2×#11762647 | C2 | semidirect |
| 5. C2×#11762646 | C2 | semidirect |
| 6. C2×#11762644 | C2 | semidirect |
| 7. C22×#10587465 | C2 | semidirect |
| 8. C2×C17×#508 | C2 | semidirect |
| 11. #11763241 | C22 | semidirect |
| 15. #11762649 | C22 | semidirect |
| 16. #11762647 | C22 | semidirect |
| 17. #11762646 | C22 | semidirect |
| 18. #11762644 | C22 | semidirect |
| 21. C2×#10587465 | C22 | semidirect |
| 24. C17×#508 | C22 | semidirect |
| 114. C2×#508 | D17 | semidirect |
| 138. #508 | C2×D17 | semidirect |
| 155. C2×C17 | #2262 | semidirect |
| 187. C17 | C2×#2262 | semidirect |
| 257. C2 | #14531091 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763241 | 2 |
| #14531091 | 2 |
| C2×#11762649 | 2 |
| C2×#11762647 | 2 |
| C2×#11762646 | 2 |
| C2×#11762644 | 2 |
| C22×#10587465 | 2 |
| C2×C17×#508 | 2 |
| C2×#2262 | 17 |