Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
464 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22569269 | C2 | semidirect |
| 3. #22558766 | C2 | semidirect |
| 4. #22558739 | C2 | semidirect |
| 5. #22558568 | C2 | semidirect |
| 6. #22558118 | C2 | semidirect |
| 7. C67×#1293 | C2 | semidirect |
| 10. #16863727 | C4 | semidirect |
| 12. #16863710 | C4 | semidirect |
| 15. #16863549 | C4 | semidirect |
| 17. #16863532 | C4 | semidirect |
| 232. #1293 | D67 | semidirect |
| 233. C67 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571025 | 2 |
| #22569269 | 2 |
| #22558766 | 2 |
| #22558739 | 2 |
| #22558568 | 2 |
| #22558118 | 2 |
| C67×#1293 | 2 |
| #9332 | 67 |