Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
412 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 412 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 |
|---|---|---|
| 4. #22558657 | C2 | semidirect |
| 5. #22558552 | C2 | semidirect |
| 6. C67⋊#1308 | C2 | semidirect |
| 7. C67×#1291 | C2 | semidirect |
| 201. #1291 | D67 | semidirect |
| 202. C67 | #9531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570382 | 2 |
| #22569194 | 2 |
| #22558838 | 2 |
| #22558657 | 2 |
| #22558552 | 2 |
| C67⋊#1308 | 2 |
| C67×#1291 | 2 |
| #9531 | 67 |