Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
300 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 3. #22561813 | C2 | semidirect |
| 5. #22558297 | C2 | semidirect |
| 6. #22558295 | C2 | semidirect |
| 7. C67×#2151 | C2 | semidirect |
| 138. #2151 | D67 | semidirect |
| 145. C67 | #13126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561836 | 2 |
| C2×#16863179 | 2 |
| #22561813 | 2 |
| #22560010 | 2 |
| #22558297 | 2 |
| #22558295 | 2 |
| C67×#2151 | 2 |
| #13126 | 67 |