Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
502 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 502 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. #14531097 | C2 | direct (N × H) |
| 3. C2×#11762647 | C2 | semidirect |
| 4. C2×#11762644 | C2 | semidirect |
| 5. C2×#11762643 | C2 | semidirect |
| 6. C22×C17×D16 | C2 | semidirect |
| 9. #11763241 | C22 | semidirect |
| 10. C2×Dic136 | C22 | semidirect |
| 12. C2×D272 | C22 | semidirect |
| 13. #11762647 | C22 | semidirect |
| 14. #11762644 | C22 | semidirect |
| 15. #11762643 | C22 | semidirect |
| 16. C2×#10587465 | C22 | semidirect |
| 21. C2×C17×D16 | C22 | semidirect |
| 43. Dic136 | C23 | semidirect |
| 46. D272 | C23 | semidirect |
| 47. #10587465 | C23 | semidirect |
| 99. C22×D16 | D17 | semidirect |
| 126. C2×D16 | C2×D17 | semidirect |
| 134. C2×C17 | #2263 | semidirect |
| 162. C17 | C2×#2263 | semidirect |
| 227. C2 | #14531097 | 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 |
| #14531097 | 2 |
| C2×#11762647 | 2 |
| C2×#11762644 | 2 |
| C2×#11762643 | 2 |
| C22×C17×D16 | 2 |
| C2×#2263 | 17 |