Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1022 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 199 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×D16×D17 | C2 | semidirect |
| 2. D17×#493 | C2 | semidirect |
| 3. #14531034 | C2 | semidirect |
| 4. #14531033 | C2 | semidirect |
| 5. #14531032 | C2 | semidirect |
| 6. C4×C16×D17 | C2 | semidirect |
| 7. C17×#2246 | C2 | semidirect |
| 11. C2×D272 | C22 | semidirect |
| 12. C2×#10587497 | C22 | semidirect |
| 15. #11763186 | C22 | semidirect |
| 18. #11763184 | C22 | semidirect |
| 20. C4×#63214 | C22 | semidirect |
| 21. C16×Dic17 | C22 | semidirect |
| 22. C2×C17×D16 | C22 | semidirect |
| 23. C17×#493 | C22 | semidirect |
| 24. C4×C16×C17 | C22 | semidirect |
| 51. C16×D17 | D4 | semidirect |
| 79. C16×C17 | C2×D4 | semidirect |
| 80. #63214 | C2×D4 | semidirect |
| 99. C4×D17 | D16 | semidirect |
| 111. #2246 | D17 | direct (N × H) |
| 121. C4×C17 | C2×D16 | semidirect |
| 125. Dic17 | C2×D16 | semidirect |
| 132. C2×D16 | C2×D17 | semidirect |
| 138. #493 | C2×D17 | semidirect |
| 142. C4×C16 | C2×D17 | semidirect |
| 147. D17 | #2246 | direct (N × H) |
| 175. C17 | C2×#2246 | semidirect |
| 204. C16 | D4×D17 | semidirect |
| 239. C4 | D16×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D17 | 2 |
| D17×#493 | 2 |
| #14531034 | 2 |
| #14531033 | 2 |
| #14531032 | 2 |
| C4×C16×D17 | 2 |
| C17×#2246 | 2 |
| C2×#2246 | 17 |