Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
438 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22569198 | C2 | semidirect |
| 3. #22558827 | C2 | semidirect |
| 4. C2×#16863135 | C2 | semidirect |
| 5. #22558560 | C2 | semidirect |
| 6. #22558109 | C2 | semidirect |
| 7. C67×#1281 | C2 | semidirect |
| 219. #1281 | D67 | semidirect |
| 220. C67 | #9265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571176 | 2 |
| #22569198 | 2 |
| #22558827 | 2 |
| C2×#16863135 | 2 |
| #22558560 | 2 |
| #22558109 | 2 |
| C67×#1281 | 2 |
| #9265 | 67 |