Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1090 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
|---|---|---|
| 2. C2×#16863839 | C2 | semidirect |
| 3. #22569864 | C2 | semidirect |
| 4. #22562162 | C2 | semidirect |
| 5. #22561946 | C2 | semidirect |
| 6. C67×#2115 | C2 | semidirect |
| 15. C22×Dic268 | C22 | semidirect |
| 18. #16863839 | C22 | semidirect |
| 21. #16863654 | C22 | semidirect |
| 23. #16863434 | C22 | semidirect |
| 25. #16863207 | C22 | semidirect |
| 27. C2×M32×C67 | C22 | semidirect |
| 28. #349×C67 | C22 | semidirect |
| 203. #2115 | D67 | semidirect |
| 204. C67 | #33532 | semidirect |
| 220. C2×M32 | C2×D67 | semidirect |
| 226. #349 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574983 | 2 |
| C2×#16863839 | 2 |
| #22569864 | 2 |
| #22562162 | 2 |
| #22561946 | 2 |
| C67×#2115 | 2 |
| #33532 | 67 |