Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22561956 | C2 | semidirect |
| 3. C2×#16863204 | C2 | semidirect |
| 4. C2×#16863179 | C2 | semidirect |
| 5. #22560256 | C2 | semidirect |
| 6. #22558312 | C2 | semidirect |
| 7. C2×#368×C67 | C2 | semidirect |
| 176. C2×#368 | D67 | semidirect |
| 182. C67 | #13392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569930 | 2 |
| #22561956 | 2 |
| C2×#16863204 | 2 |
| C2×#16863179 | 2 |
| #22560256 | 2 |
| #22558312 | 2 |
| C2×#368×C67 | 2 |
| #13392 | 67 |