Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#16863133 | C2 | semidirect |
| 5. #22558096 | C2 | semidirect |
| 6. #22558051 | C2 | semidirect |
| 7. C67×#1472 | C2 | semidirect |
| 10. #16863726 | C4 | semidirect |
| 11. #16863709 | C4 | semidirect |
| 15. #16863552 | C4 | semidirect |
| 16. #16863535 | C4 | semidirect |
| 238. #1472 | D67 | semidirect |
| 241. C67 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570990 | 2 |
| #22569263 | 2 |
| #22558714 | 2 |
| C2×#16863133 | 2 |
| #22558096 | 2 |
| #22558051 | 2 |
| C67×#1472 | 2 |
| #9263 | 67 |