Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
462 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #22558811 | C2 | semidirect |
| 5. #22558073 | C2 | semidirect |
| 6. #22558065 | C2 | semidirect |
| 7. C67×#2336 | C2 | semidirect |
| 9. #16863806 | C4 | semidirect |
| 10. #16863762 | C4 | semidirect |
| 199. #2336 | D67 | semidirect |
| 205. C67 | #9382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571399 | 2 |
| #22561127 | 2 |
| #22558811 | 2 |
| #22558755 | 2 |
| #22558073 | 2 |
| #22558065 | 2 |
| C67×#2336 | 2 |
| #9382 | 67 |