Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
386 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22558907 | C2 | semidirect |
| 4. #22558720 | C2 | semidirect |
| 6. #22558079 | C2 | semidirect |
| 7. C67×#1843 | C2 | semidirect |
| 159. #1843 | D67 | semidirect |
| 165. C67 | #10514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571526 | 2 |
| #22558907 | 2 |
| #22558902 | 2 |
| #22558720 | 2 |
| #22558716 | 2 |
| #22558079 | 2 |
| C67×#1843 | 2 |
| #10514 | 67 |