Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22569150 | C2 | semidirect |
| 5. #22558067 | C2 | semidirect |
| 6. #22558039 | C2 | semidirect |
| 7. C67×#1518 | C2 | semidirect |
| 9. #16863770 | C4 | semidirect |
| 10. #16863744 | C4 | semidirect |
| 89. C2×C67⋊C8 | SD16 | semidirect |
| 181. #1518 | D67 | semidirect |
| 184. C67 | #9294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571147 | 2 |
| #22569150 | 2 |
| #22561032 | 2 |
| #22558876 | 2 |
| #22558067 | 2 |
| #22558039 | 2 |
| C67×#1518 | 2 |
| #9294 | 67 |