Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 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×#11763246 | C2 | semidirect |
| 2. #14539213 | C2 | semidirect |
| 3. D17×#493 | C2 | semidirect |
| 4. #14531049 | C2 | semidirect |
| 5. #14531041 | C2 | semidirect |
| 6. #14531034 | C2 | semidirect |
| 7. #14531033 | C2 | semidirect |
| 8. C4×#10587469 | C2 | semidirect |
| 9. C17×#2248 | C2 | semidirect |
| 17. C2×#10587499 | C22 | semidirect |
| 18. C2×D272 | C22 | semidirect |
| 19. C2×#10587497 | C22 | semidirect |
| 22. #11763194 | C22 | semidirect |
| 24. #11763186 | C22 | semidirect |
| 30. #11762584 | C22 | semidirect |
| 31. C4×#63214 | C22 | semidirect |
| 32. C2×C17×SD32 | C22 | semidirect |
| 33. C17×#494 | C22 | semidirect |
| 35. C4×C16×C17 | C22 | semidirect |
| 77. #10587469 | D4 | semidirect |
| 120. C16×C17 | C2×D4 | semidirect |
| 121. #63214 | C2×D4 | semidirect |
| 161. #2248 | D17 | semidirect |
| 176. C4×C17 | #509 | semidirect |
| 189. C2×SD32 | C2×D17 | semidirect |
| 195. #494 | C2×D17 | semidirect |
| 206. C4×C16 | C2×D17 | semidirect |
| 255. C17 | #33717 | semidirect |
| 299. C16 | D4×D17 | semidirect |
| 346. C4 | #11763246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763246 | 2 |
| #14539213 | 2 |
| D17×#493 | 2 |
| #14531049 | 2 |
| #14531041 | 2 |
| #14531034 | 2 |
| #14531033 | 2 |
| C4×#10587469 | 2 |
| C17×#2248 | 2 |
| #33717 | 17 |