Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 520 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. #22562377 | C2 | semidirect |
| 4. #22562287 | C2 | semidirect |
| 6. #22562098 | C2 | semidirect |
| 7. #22562021 | C2 | semidirect |
| 8. C67×#3185 | C2 | semidirect |
| 18. #16863218 | C22 | semidirect |
| 19. #16863217 | C22 | semidirect |
| 20. #16863212 | C22 | semidirect |
| 23. #16863174 | C22 | semidirect |
| 25. #498×C67 | C22 | semidirect |
| 26. #494×C67 | C22 | semidirect |
| 31. #441×C67 | C22 | semidirect |
| 162. #3185 | D67 | semidirect |
| 170. C67 | #33689 | semidirect |
| 175. #498 | C2×D67 | semidirect |
| 176. #494 | C2×D67 | semidirect |
| 185. #441 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569120 | 2 |
| #22562426 | 2 |
| #22562377 | 2 |
| #22562287 | 2 |
| #22562159 | 2 |
| #22562098 | 2 |
| #22562021 | 2 |
| C67×#3185 | 2 |
| #33689 | 67 |