Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
412 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22561974 | C2 | semidirect |
| 5. #22560334 | C2 | semidirect |
| 6. #22558310 | C2 | semidirect |
| 7. C67×#1389 | C2 | semidirect |
| 11. #16863507 | C4 | semidirect |
| 143. #1389 | D67 | semidirect |
| 145. C67 | #12826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569060 | 2 |
| #22561974 | 2 |
| C2×#16863208 | 2 |
| #22561926 | 2 |
| #22560334 | 2 |
| #22558310 | 2 |
| C67×#1389 | 2 |
| #12826 | 67 |