Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
856 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22561894 | C2 | semidirect |
| 3. #22561858 | C2 | semidirect |
| 4. #22560756 | C2 | semidirect |
| 5. C67×#1884 | C2 | semidirect |
| 7. #16864138 | C4 | semidirect |
| 11. #16864031 | C4 | semidirect |
| 16. #16863380 | C22 | semidirect |
| 22. #568×C67 | C22 | semidirect |
| 25. #410×C67 | C22 | semidirect |
| 211. #1884 | D67 | semidirect |
| 212. C67 | #12769 | semidirect |
| 213. #568 | C2×D67 | semidirect |
| 228. #410 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574614 | 2 |
| #22561894 | 2 |
| #22561858 | 2 |
| #22560756 | 2 |
| C67×#1884 | 2 |
| #12769 | 67 |