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. C22×D272 | C2 | semidirect |
| 2. #14531096 | C2 | direct (N × H) |
| 3. C2×#11762646 | C2 | semidirect |
| 4. C2×#11762644 | C2 | semidirect |
| 5. C2×#11762643 | C2 | semidirect |
| 6. C2×C17×#508 | C2 | semidirect |
| 11. C2×D272 | C22 | semidirect |
| 12. #11762646 | C22 | semidirect |
| 13. #11762644 | C22 | semidirect |
| 14. #11762643 | C22 | semidirect |
| 15. C2×#10587465 | C22 | semidirect |
| 18. C17×#508 | C22 | semidirect |
| 19. C2×C17×Q32 | C22 | semidirect |
| 21. C2×C17×D16 | C22 | semidirect |
| 36. C17×Q32 | C23 | semidirect |
| 39. C17×D16 | C23 | semidirect |
| 47. #10587465 | C23 | semidirect |
| 98. C2×#508 | D17 | semidirect |
| 119. #508 | C2×D17 | semidirect |
| 120. C2×Q32 | C2×D17 | semidirect |
| 126. C2×D16 | C2×D17 | semidirect |
| 134. C2×C17 | #2263 | semidirect |
| 150. Q32 | C22×D17 | semidirect |
| 156. D16 | C22×D17 | semidirect |
| 162. C17 | C2×#2263 | semidirect |
| 227. C2 | #14531096 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D272 | 2 |
| #14531096 | 2 |
| C2×#11762646 | 2 |
| C2×#11762644 | 2 |
| C2×#11762643 | 2 |
| C2×C17×#508 | 2 |
| C2×#2263 | 17 |