Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
438 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 438 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. #22569198 | C2 | semidirect |
| 3. #22558830 | C2 | semidirect |
| 4. C2×#16863136 | C2 | semidirect |
| 5. #22558107 | C2 | semidirect |
| 6. #22558053 | C2 | semidirect |
| 7. C67×#1469 | C2 | semidirect |
| 217. #1469 | D67 | semidirect |
| 220. C67 | #9265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571174 | 2 |
| #22569198 | 2 |
| #22558830 | 2 |
| C2×#16863136 | 2 |
| #22558107 | 2 |
| #22558053 | 2 |
| C67×#1469 | 2 |
| #9265 | 67 |