Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1314 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1314 conjugacy classes of subgroups — too many to draw. Only its 191 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. #22570603 | C2 | semidirect |
| 3. #22565382 | C2 | semidirect |
| 4. #22561439 | C2 | semidirect |
| 5. #22561128 | C2 | semidirect |
| 6. #22560165 | C2 | semidirect |
| 7. C4×#100×C67 | C2 | semidirect |
| 15. C2×#14524043 | C22 | semidirect |
| 20. C2×#14523969 | C22 | semidirect |
| 21. #16863398 | C22 | semidirect |
| 24. #16863261 | C22 | semidirect |
| 26. C4×C4⋊Dic67 | C22 | semidirect |
| 29. C4×M16×C67 | C22 | semidirect |
| 30. #343×C67 | C22 | semidirect |
| 206. C4×#100 | D67 | semidirect |
| 207. C67 | #25869 | semidirect |
| 224. C4×M16 | C2×D67 | semidirect |
| 230. #343 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573973 | 2 |
| #22570603 | 2 |
| #22565382 | 2 |
| #22561439 | 2 |
| #22561128 | 2 |
| #22560165 | 2 |
| C4×#100×C67 | 2 |
| #25869 | 67 |