Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
406 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22571819 | C2 | semidirect |
| 2. #22562475 | C2 | semidirect |
| 3. #22562244 | C2 | semidirect |
| 4. #22559689 | C2 | semidirect |
| 5. #22558251 | C2 | semidirect |
| 6. #22558168 | C2 | semidirect |
| 7. C67×#1333 | C2 | semidirect |
| 14. #16863773 | C22 | semidirect |
| 21. C4⋊(C67⋊C16) | C22 | semidirect |
| 25. #346×C67 | C22 | semidirect |
| 26. #334×C67 | C22 | semidirect |
| 106. D8×C67 | D8 | semidirect |
| 185. #1333 | D67 | semidirect |
| 187. C67 | #12324 | semidirect |
| 204. #346 | C2×D67 | semidirect |
| 205. #334 | C2×D67 | semidirect |
| 275. D8 | D536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571819 | 2 |
| #22562475 | 2 |
| #22562244 | 2 |
| #22559689 | 2 |
| #22558251 | 2 |
| #22558168 | 2 |
| C67×#1333 | 2 |
| #12324 | 67 |