Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
544 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22563126 | C2 | semidirect |
| 5. #22558603 | C2 | semidirect |
| 6. #22558110 | C2 | semidirect |
| 7. C67×#1286 | C2 | semidirect |
| 13. #16863607 | C4 | semidirect |
| 14. #16863597 | C4 | semidirect |
| 208. #1286 | D67 | semidirect |
| 209. C67 | #9180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569683 | 2 |
| #22563126 | 2 |
| #22558768 | 2 |
| #22558705 | 2 |
| #22558603 | 2 |
| #22558110 | 2 |
| C67×#1286 | 2 |
| #9180 | 67 |