Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
378 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 378 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. #22561974 | C2 | semidirect |
| 4. #22561125 | C2 | semidirect |
| 6. #22558325 | C2 | semidirect |
| 7. C67×#2141 | C2 | semidirect |
| 166. #2141 | D67 | semidirect |
| 170. C67 | #13443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863837 | 2 |
| #22561974 | 2 |
| #22561959 | 2 |
| #22561125 | 2 |
| #22561105 | 2 |
| #22558325 | 2 |
| C67×#2141 | 2 |
| #13443 | 67 |