Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
500 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #22560673 | C2 | semidirect |
| 3. #22560670 | C2 | semidirect |
| 4. #22560394 | C2 | semidirect |
| 5. #22558724 | C2 | semidirect |
| 6. #22558085 | C2 | semidirect |
| 7. C67×#1507 | C2 | semidirect |
| 238. #1507 | D67 | semidirect |
| 240. C67 | #10557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570957 | 2 |
| #22560673 | 2 |
| #22560670 | 2 |
| #22560394 | 2 |
| #22558724 | 2 |
| #22558085 | 2 |
| C67×#1507 | 2 |
| #10557 | 67 |