Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
438 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 438 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. #22558829 | C2 | semidirect |
| 3. C2×#16863135 | C2 | semidirect |
| 4. #22558560 | C2 | semidirect |
| 5. #22558108 | C2 | semidirect |
| 6. #22558053 | C2 | semidirect |
| 7. C67×#2968 | C2 | semidirect |
| 214. #2968 | 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 |
|---|---|
| #22571170 | 2 |
| #22558829 | 2 |
| C2×#16863135 | 2 |
| #22558560 | 2 |
| #22558108 | 2 |
| #22558053 | 2 |
| C67×#2968 | 2 |
| #9265 | 67 |