Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 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. #22558823 | C2 | semidirect |
| 5. #22558683 | C2 | semidirect |
| 6. #22558071 | C2 | semidirect |
| 7. C67×#1275 | C2 | semidirect |
| 174. #1275 | D67 | semidirect |
| 175. C67 | #9285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571167 | 2 |
| #22569284 | 2 |
| #22558823 | 2 |
| #22558819 | 2 |
| #22558683 | 2 |
| #22558071 | 2 |
| C67×#1275 | 2 |
| #9285 | 67 |