Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
338 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 4. #22560382 | C2 | semidirect |
| 5. #22558307 | C2 | semidirect |
| 6. #22558292 | C2 | semidirect |
| 7. C67×#1383 | C2 | semidirect |
| 141. #1383 | D67 | semidirect |
| 143. C67 | #13487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863210 | 2 |
| C2×#16863208 | 2 |
| #22561083 | 2 |
| #22560382 | 2 |
| #22558307 | 2 |
| #22558292 | 2 |
| C67×#1383 | 2 |
| #13487 | 67 |