Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
926 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#16863210 | C2 | semidirect |
| 3. #22561938 | C2 | semidirect |
| 4. #22560259 | C2 | semidirect |
| 5. C67×#2115 | C2 | semidirect |
| 15. C2×#14523979 | C22 | semidirect |
| 21. C2×M32×C67 | C22 | semidirect |
| 178. #2115 | D67 | semidirect |
| 180. C67 | #12743 | semidirect |
| 191. C2×M32 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864201 | 2 |
| C2×#16863210 | 2 |
| #22561938 | 2 |
| #22560259 | 2 |
| C67×#2115 | 2 |
| #12743 | 67 |