Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
470 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 470 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 |
|---|---|---|
| 2. #22568869 | C2 | semidirect |
| 3. #22560301 | C2 | semidirect |
| 6. #22558096 | C2 | semidirect |
| 7. C67×#1305 | C2 | semidirect |
| 17. #16863438 | C4 | semidirect |
| 18. #16863438 | C4 | semidirect |
| 20. #16863402 | C4 | semidirect |
| 21. #16863402 | C4 | semidirect |
| 228. #1305 | D67 | semidirect |
| 230. C67 | #9348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570150 | 2 |
| #22568869 | 2 |
| #22560301 | 2 |
| #22558776 | 2 |
| #22558570 | 2 |
| #22558096 | 2 |
| C67×#1305 | 2 |
| #9348 | 67 |