Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
686 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22558728 | C2 | semidirect |
| 5. #22558572 | C2 | semidirect |
| 6. #22558086 | C2 | semidirect |
| 7. C67×#1282 | C2 | semidirect |
| 9. C22×Dic268 | C4 | semidirect |
| 10. C22×#11761617 | C4 | semidirect |
| 19. C2×#14523968 | C4 | semidirect |
| 20. C2×#14523965 | C4 | semidirect |
| 278. #1282 | D67 | semidirect |
| 279. C67 | #9239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863560 | 2 |
| #22568655 | 2 |
| #22560154 | 2 |
| #22558728 | 2 |
| #22558572 | 2 |
| #22558086 | 2 |
| C67×#1282 | 2 |
| #9239 | 67 |