Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1004 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1004 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. #22571147 | C2 | semidirect |
| 3. #22559287 | C2 | semidirect |
| 4. #22559268 | C2 | semidirect |
| 5. #22558871 | C2 | semidirect |
| 6. #22558630 | C2 | semidirect |
| 7. C67×#3550 | C2 | semidirect |
| 19. #16863145 | C22 | semidirect |
| 20. #16863140 | C22 | semidirect |
| 21. Q8⋊(C67⋊C8) | C22 | semidirect |
| 23. #559×C67 | C22 | semidirect |
| 24. Q82×C67 | C22 | semidirect |
| 168. #3550 | D67 | semidirect |
| 175. C67 | #18718 | semidirect |
| 178. #559 | C2×D67 | semidirect |
| 179. Q82 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571147 | 2 |
| #22570662 | 2 |
| #22559287 | 2 |
| #22559268 | 2 |
| #22558871 | 2 |
| #22558630 | 2 |
| C67×#3550 | 2 |
| #18718 | 67 |