Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. C2×#16863212 | C2 | semidirect |
| 5. #22561000 | C2 | semidirect |
| 6. #22558294 | C2 | semidirect |
| 7. C2×#362×C67 | C2 | semidirect |
| 172. C2×#362 | D67 | semidirect |
| 176. C67 | #13418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570698 | 2 |
| #22561959 | 2 |
| C2×#16863212 | 2 |
| #22561936 | 2 |
| #22561000 | 2 |
| #22558294 | 2 |
| C2×#362×C67 | 2 |
| #13418 | 67 |