Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22562426 | C2 | semidirect |
| 3. #22562382 | C2 | semidirect |
| 4. #22562287 | C2 | semidirect |
| 6. #22562098 | C2 | semidirect |
| 7. #22562025 | C2 | semidirect |
| 8. C67×#3177 | C2 | semidirect |
| 18. #16863218 | C22 | semidirect |
| 19. #16863217 | C22 | semidirect |
| 20. #16863212 | C22 | semidirect |
| 23. #16863174 | C22 | semidirect |
| 25. #499×C67 | C22 | semidirect |
| 26. #494×C67 | C22 | semidirect |
| 30. #441×C67 | C22 | semidirect |
| 161. #3177 | D67 | semidirect |
| 169. C67 | #33693 | semidirect |
| 174. #499 | C2×D67 | semidirect |
| 175. #494 | C2×D67 | semidirect |
| 183. #441 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569113 | 2 |
| #22562426 | 2 |
| #22562382 | 2 |
| #22562287 | 2 |
| #22562159 | 2 |
| #22562098 | 2 |
| #22562025 | 2 |
| C67×#3177 | 2 |
| #33693 | 67 |