Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
460 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #22560012 | C2 | semidirect |
| 5. #22560011 | C2 | semidirect |
| 6. #22558338 | C2 | semidirect |
| 7. C67×#1395 | C2 | semidirect |
| 8. C2×#14524051 | C4 | semidirect |
| 15. #16863419 | C4 | semidirect |
| 18. #16863362 | C4 | semidirect |
| 21. C2×C8×Dic67 | C4 | semidirect |
| 22. #16863194 | C4 | semidirect |
| 23. #16863192 | C4 | semidirect |
| 212. #1395 | D67 | semidirect |
| 213. C67 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568917 | 2 |
| #22561892 | 2 |
| #22561872 | 2 |
| #22560012 | 2 |
| #22560011 | 2 |
| #22558338 | 2 |
| C67×#1395 | 2 |
| #12633 | 67 |