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 |
|---|---|---|
| 1. #22561975 | C2 | semidirect |
| 4. C2×#16863173 | C2 | semidirect |
| 6. #22558292 | C2 | semidirect |
| 7. C67×#1378 | C2 | semidirect |
| 144. #1378 | D67 | semidirect |
| 146. C67 | #13127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561975 | 2 |
| #22561838 | 2 |
| #22561829 | 2 |
| C2×#16863173 | 2 |
| #22560055 | 2 |
| #22558292 | 2 |
| C67×#1378 | 2 |
| #13127 | 67 |