Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1004 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22574623 | C2 | semidirect |
| 2. #22571152 | C2 | semidirect |
| 4. #22559288 | C2 | semidirect |
| 5. #22559269 | C2 | semidirect |
| 6. #22558629 | C2 | semidirect |
| 7. C67×#1543 | C2 | semidirect |
| 10. #16864132 | C22 | semidirect |
| 11. #16864126 | C22 | semidirect |
| 26. #16863126 | C22 | semidirect |
| 29. #333×C67 | C22 | semidirect |
| 30. #331×C67 | C22 | semidirect |
| 173. #1543 | D67 | semidirect |
| 175. C67 | #18718 | semidirect |
| 196. #333 | C2×D67 | semidirect |
| 197. #331 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574623 | 2 |
| #22571152 | 2 |
| #22570662 | 2 |
| #22559288 | 2 |
| #22559269 | 2 |
| #22558629 | 2 |
| C67×#1543 | 2 |
| #18718 | 67 |