Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
920 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 175 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. #22570758 | C2 | semidirect |
| 5. #22561190 | C2 | semidirect |
| 6. #22561054 | C2 | semidirect |
| 7. #22560423 | C2 | semidirect |
| 9. C67×#2642 | C2 | semidirect |
| 192. #2642 | D67 | semidirect |
| 198. C67 | #25691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574093 | 2 |
| #22570758 | 2 |
| #22570027 | 2 |
| #22561426 | 2 |
| #22561190 | 2 |
| #22561054 | 2 |
| #22560423 | 2 |
| #22560020 | 2 |
| C67×#2642 | 2 |
| #25691 | 67 |