Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
392 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 2. #22561964 | C2 | semidirect |
| 3. #22561959 | C2 | semidirect |
| 4. #22561098 | C2 | semidirect |
| 5. #22561095 | C2 | semidirect |
| 6. #22558312 | C2 | semidirect |
| 7. C67×#2148 | C2 | semidirect |
| 185. #2148 | D67 | semidirect |
| 189. C67 | #13444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573343 | 2 |
| #22561964 | 2 |
| #22561959 | 2 |
| #22561098 | 2 |
| #22561095 | 2 |
| #22558312 | 2 |
| C67×#2148 | 2 |
| #13444 | 67 |