Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1066 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 155 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. #22571214 | C2 | semidirect |
| 3. #22570595 | C2 | semidirect |
| 4. #22559517 | C2 | semidirect |
| 5. #22558808 | C2 | semidirect |
| 6. C67×#1533 | C2 | semidirect |
| 10. #16863953 | C22 | semidirect |
| 16. #16863790 | C22 | semidirect |
| 17. #16863756 | C22 | semidirect |
| 18. #16863755 | C22 | semidirect |
| 25. C4×#11761612 | C22 | semidirect |
| 26. #16863135 | C22 | semidirect |
| 28. #432×C67 | C22 | semidirect |
| 29. #329×C67 | C22 | semidirect |
| 38. #14524043 | C23 | semidirect |
| 64. #14523954 | C23 | semidirect |
| 75. #97×C67 | C23 | semidirect |
| 187. #1533 | D67 | semidirect |
| 189. C67 | #18997 | semidirect |
| 207. #432 | C2×D67 | semidirect |
| 212. #329 | C2×D67 | semidirect |
| 257. #97 | C22×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864138 | 2 |
| #22571214 | 2 |
| #22570595 | 2 |
| #22559517 | 2 |
| #22558808 | 2 |
| C67×#1533 | 2 |
| #18997 | 67 |