Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
454 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22561958 | C2 | semidirect |
| 3. C2×#16863210 | C2 | semidirect |
| 4. C2×#16863208 | C2 | semidirect |
| 5. #22561000 | C2 | semidirect |
| 6. #22558296 | C2 | semidirect |
| 7. C67×#2143 | C2 | semidirect |
| 67. #108×C67 | D4 | semidirect |
| 179. #2143 | D67 | semidirect |
| 182. C67 | #13417 | semidirect |
| 240. #108 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570696 | 2 |
| #22561958 | 2 |
| C2×#16863210 | 2 |
| C2×#16863208 | 2 |
| #22561000 | 2 |
| #22558296 | 2 |
| C67×#2143 | 2 |
| #13417 | 67 |