Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
442 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22558223 | C2 | semidirect |
| 4. C67×#1810 | C2 | semidirect |
| 15. C22⋊(C67⋊C16) | C22 | semidirect |
| 19. #341×C67 | C22 | semidirect |
| 153. #1810 | D67 | semidirect |
| 155. C67 | #11895 | semidirect |
| 170. #341 | 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 |
| #22558223 | 2 |
| C67×#1810 | 2 |
| #11895 | 67 |