Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 4. #22558847 | C2 | semidirect |
| 5. #22558079 | C2 | semidirect |
| 6. #22558071 | C2 | semidirect |
| 7. C67×#1481 | C2 | semidirect |
| 168. #1481 | D67 | semidirect |
| 171. C67 | #9373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571216 | 2 |
| #22569284 | 2 |
| #22558902 | 2 |
| #22558847 | 2 |
| #22558079 | 2 |
| #22558071 | 2 |
| C67×#1481 | 2 |
| #9373 | 67 |