Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
598 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22571327 | C2 | semidirect |
| 3. #22570668 | C2 | semidirect |
| 4. #22561161 | C2 | semidirect |
| 5. #22558703 | C2 | semidirect |
| 6. #22558060 | C2 | semidirect |
| 7. C67×#1980 | C2 | semidirect |
| 118. M16×C67 | D8 | semidirect |
| 208. #1980 | D67 | semidirect |
| 211. C67 | #10204 | semidirect |
| 311. M16 | #11761613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571516 | 2 |
| #22571327 | 2 |
| #22570668 | 2 |
| #22561161 | 2 |
| #22558703 | 2 |
| #22558060 | 2 |
| C67×#1980 | 2 |
| #10204 | 67 |