Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
556 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. #22571596 | C2 | semidirect |
| 3. #22570584 | C2 | semidirect |
| 4. #22561049 | C2 | semidirect |
| 5. #22558631 | C2 | semidirect |
| 6. #22558099 | C2 | semidirect |
| 7. C67×#1525 | C2 | semidirect |
| 197. #1525 | D67 | semidirect |
| 200. C67 | #10112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571596 | 2 |
| #22571124 | 2 |
| #22570584 | 2 |
| #22561049 | 2 |
| #22558631 | 2 |
| #22558099 | 2 |
| C67×#1525 | 2 |
| #10112 | 67 |