Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
566 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#16863210 | C2 | semidirect |
| 4. C2×#16863209 | C2 | semidirect |
| 5. C2×#16863208 | C2 | semidirect |
| 6. #108×Dic67 | C2 | semidirect |
| 7. C2×#361×C67 | C2 | semidirect |
| 47. #14523979 | D4 | semidirect |
| 65. #108×C67 | D4 | semidirect |
| 166. Dic67 | #361 | semidirect |
| 179. C2×#361 | D67 | semidirect |
| 181. C67 | #13257 | semidirect |
| 235. #108 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863771 | 2 |
| #22561964 | 2 |
| C2×#16863210 | 2 |
| C2×#16863209 | 2 |
| C2×#16863208 | 2 |
| #108×Dic67 | 2 |
| C2×#361×C67 | 2 |
| #13257 | 67 |