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 |
|---|---|---|
| 2. #22568869 | C2 | semidirect |
| 3. #22560309 | C2 | semidirect |
| 5. #22558085 | C2 | semidirect |
| 6. #22558057 | C2 | semidirect |
| 16. C2×#14523976 | C4 | semidirect |
| 17. C2×#14523974 | C4 | semidirect |
| 19. C2×#14523964 | C4 | semidirect |
| 20. C2×#14523964 | C4 | semidirect |
| 231. C67 | #9242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863717 | 2 |
| #22568869 | 2 |
| #22560309 | 2 |
| #22558569 | 2 |
| #22558085 | 2 |
| #22558057 | 2 |
| C67×#1507 | 2 |
| #9242 | 67 |