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. C22×D272 | C2 | semidirect |
| 3. #14531099 | C2 | direct (N × H) |
| 4. C2×#11762648 | C2 | semidirect |
| 5. C2×D544 | C2 | semidirect |
| 6. C2×C17×M64 | C2 | semidirect |
| 10. #11763241 | C22 | semidirect |
| 11. C2×Dic136 | C22 | semidirect |
| 16. C2×D272 | C22 | semidirect |
| 17. C2×D272 | C22 | semidirect |
| 18. #11762648 | C22 | semidirect |
| 19. D544 | C22 | semidirect |
| 21. C17×M64 | C22 | semidirect |
| 22. C2×C17×C32 | C22 | semidirect |
| 40. Dic136 | C23 | semidirect |
| 46. D272 | C23 | semidirect |
| 47. C17×C32 | C23 | semidirect |
| 103. C2×M64 | D17 | semidirect |
| 130. M64 | C2×D17 | semidirect |
| 131. C2×C32 | C2×D17 | semidirect |
| 133. C2×C17 | #2263 | semidirect |
| 161. C32 | C22×D17 | semidirect |
| 162. C17 | C2×#2263 | semidirect |
| 227. C2 | #14531099 | 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 |
| C22×D272 | 2 |
| #14531099 | 2 |
| C2×#11762648 | 2 |
| C2×D544 | 2 |
| C2×C17×M64 | 2 |
| C2×#2263 | 17 |