Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1214 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 187 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. #22570140 | C2 | semidirect |
| 3. #22561426 | C2 | semidirect |
| 4. #22560657 | C2 | semidirect |
| 5. #22560423 | C2 | semidirect |
| 6. #22560167 | C2 | semidirect |
| 7. #22560133 | C2 | semidirect |
| 8. C67×#2310 | C2 | semidirect |
| 207. #2310 | D67 | semidirect |
| 213. C67 | #24023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573860 | 2 |
| #22570140 | 2 |
| #22561426 | 2 |
| #22560657 | 2 |
| #22560423 | 2 |
| #22560167 | 2 |
| #22560133 | 2 |
| C67×#2310 | 2 |
| #24023 | 67 |