Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22569379 | C2 | semidirect |
| 3. #22561041 | C2 | semidirect |
| 4. #22558679 | C2 | semidirect |
| 5. #22558102 | C2 | semidirect |
| 6. #22558100 | C2 | semidirect |
| 7. C67×#1500 | C2 | semidirect |
| 9. #16863806 | C4 | semidirect |
| 10. #16863786 | C4 | semidirect |
| 11. #16863762 | C4 | semidirect |
| 12. #16863755 | C4 | semidirect |
| 219. #1500 | D67 | semidirect |
| 223. C67 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570805 | 2 |
| #22569379 | 2 |
| #22561041 | 2 |
| #22558679 | 2 |
| #22558102 | 2 |
| #22558100 | 2 |
| C67×#1500 | 2 |
| #8997 | 67 |