Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
646 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22568671 | C2 | semidirect |
| 3. #22561859 | C2 | semidirect |
| 4. #22560182 | C2 | semidirect |
| 5. #22558337 | C2 | semidirect |
| 6. #22558329 | C2 | semidirect |
| 7. C67×#2128 | C2 | semidirect |
| 9. C2×#14524069 | C4 | semidirect |
| 10. C22×#11761616 | C4 | semidirect |
| 18. #16863404 | C4 | semidirect |
| 19. #16863390 | C4 | semidirect |
| 250. #2128 | D67 | semidirect |
| 255. C67 | #13103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569493 | 2 |
| #22568671 | 2 |
| #22561859 | 2 |
| #22560182 | 2 |
| #22558337 | 2 |
| #22558329 | 2 |
| C67×#2128 | 2 |
| #13103 | 67 |