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×#11763243 | C2 | semidirect |
| 2. #14539211 | C2 | semidirect |
| 3. D17×#493 | C2 | semidirect |
| 4. #14531047 | C2 | semidirect |
| 5. #14531040 | C2 | semidirect |
| 6. #14531039 | C2 | semidirect |
| 7. #14531033 | C2 | semidirect |
| 8. C4×#10587469 | C2 | semidirect |
| 9. C17×#2246 | C2 | semidirect |
| 17. C2×#10587471 | C22 | semidirect |
| 18. C2×#10587498 | C22 | semidirect |
| 19. C2×#10587497 | C22 | semidirect |
| 22. #11763192 | C22 | semidirect |
| 23. #11763189 | C22 | semidirect |
| 30. #11762584 | C22 | semidirect |
| 31. C4×#63214 | C22 | semidirect |
| 32. C2×C17×D16 | C22 | semidirect |
| 34. C17×#493 | C22 | semidirect |
| 35. C4×C16×C17 | C22 | semidirect |
| 77. #10587469 | D4 | semidirect |
| 120. C16×C17 | C2×D4 | semidirect |
| 121. #63214 | C2×D4 | semidirect |
| 163. #2246 | D17 | semidirect |
| 175. C4×C17 | #509 | semidirect |
| 191. C2×D16 | C2×D17 | semidirect |
| 201. #493 | C2×D17 | semidirect |
| 206. C4×C16 | C2×D17 | semidirect |
| 255. C17 | #33717 | semidirect |
| 299. C16 | D4×D17 | semidirect |
| 346. C4 | #11763243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763243 | 2 |
| #14539211 | 2 |
| D17×#493 | 2 |
| #14531047 | 2 |
| #14531040 | 2 |
| #14531039 | 2 |
| #14531033 | 2 |
| C4×#10587469 | 2 |
| C17×#2246 | 2 |
| #33717 | 17 |