Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
464 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22561820 | C2 | semidirect |
| 3. #22558217 | C2 | semidirect |
| 4. C67×#1807 | C2 | semidirect |
| 5. C22×D536 | C4 | semidirect |
| 10. #16863632 | C4 | semidirect |
| 12. C2×#14523977 | C4 | semidirect |
| 15. C22⋊(C67⋊C16) | C22 | semidirect |
| 19. #340×C67 | C22 | semidirect |
| 157. #1807 | D67 | semidirect |
| 159. C67 | #11888 | semidirect |
| 174. #340 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863632 | 2 |
| #22561820 | 2 |
| #22558217 | 2 |
| C67×#1807 | 2 |
| #11888 | 67 |