Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
280 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22562024 | C2 | semidirect |
| 3. #22561973 | C2 | semidirect |
| 4. #22558271 | C2 | semidirect |
| 5. #22558269 | C2 | semidirect |
| 6. #22558250 | C2 | semidirect |
| 7. C67×#1359 | C2 | semidirect |
| 146. #1359 | D67 | semidirect |
| 147. C67 | #11991 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570834 | 2 |
| #22562024 | 2 |
| #22561973 | 2 |
| #22558271 | 2 |
| #22558269 | 2 |
| #22558250 | 2 |
| C67×#1359 | 2 |
| #11991 | 67 |