Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
5942 conjugacy classes of subgroups; only the 387 normal subgroups are shown.
This group has 5942 conjugacy classes of subgroups — too many to draw. Only its 387 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 |
|---|---|---|
| 1. C2×#16863547 | C2 | semidirect |
| 2. #22568496 | C2 | semidirect |
| 3. #22560140 | C2 | semidirect |
| 4. #22560119 | C2 | semidirect |
| 6. C22×#11761616 | C22 | semidirect |
| 7. C2×#14524022 | C22 | semidirect |
| 9. C2×#14523964 | C22 | semidirect |
| 10. C2×C22⋊(C67⋊C8) | C22 | semidirect |
| 12. #16863256 | C22 | semidirect |
| 19. C22×Dic134 | C23 | semidirect |
| 21. C22×C67⋊C8 | C23 | semidirect |
| 23. C2×C4⋊Dic67 | C23 | semidirect |
| 66. C24×C67 | SD16 | semidirect |
| 122. C22×C67 | #450 | semidirect |
| 141. C67 | #32881 | semidirect |
| 193. C24 | #11761616 | semidirect |
| 258. C22 | #16863547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863547 | 2 |
| #22568496 | 2 |
| #22560140 | 2 |
| #22560119 | 2 |
| C24×D4×C67 | 2 |
| #32881 | 67 |