Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
478 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22561199 | C2 | semidirect |
| 4. #22558964 | C2 | semidirect |
| 6. #22558490 | C2 | semidirect |
| 7. C67×#1549 | C2 | semidirect |
| 155. #1549 | D67 | semidirect |
| 158. C67 | #9800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863744 | 2 |
| #22561199 | 2 |
| #22561048 | 2 |
| #22558964 | 2 |
| #22558876 | 2 |
| #22558490 | 2 |
| C67×#1549 | 2 |
| #9800 | 67 |