Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #22558974 | C2 | semidirect |
| 5. #22558103 | C2 | semidirect |
| 6. #22558101 | C2 | semidirect |
| 7. C67×#1569 | C2 | semidirect |
| 22. #16863135 | C4 | semidirect |
| 23. #16863135 | C4 | semidirect |
| 24. #16863135 | C4 | semidirect |
| 25. #16863135 | C4 | semidirect |
| 190. #1569 | D67 | semidirect |
| 194. C67 | #8918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569279 | 2 |
| #22561040 | 2 |
| #22558974 | 2 |
| #22558800 | 2 |
| #22558103 | 2 |
| #22558101 | 2 |
| C67×#1569 | 2 |
| #8918 | 67 |