Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
386 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 386 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. C2×#16863225 | C2 | semidirect |
| 3. C2×#16863203 | C2 | semidirect |
| 4. C2×#16863181 | C2 | semidirect |
| 5. #22560256 | C2 | semidirect |
| 6. #22558313 | C2 | semidirect |
| 7. C67×#2148 | C2 | semidirect |
| 177. #2148 | 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 |
|---|---|
| #22569925 | 2 |
| C2×#16863225 | 2 |
| C2×#16863203 | 2 |
| C2×#16863181 | 2 |
| #22560256 | 2 |
| #22558313 | 2 |
| C67×#2148 | 2 |
| #13392 | 67 |