Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
466 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #22558682 | C2 | semidirect |
| 5. #22558553 | C2 | semidirect |
| 6. #22558070 | C2 | semidirect |
| 7. C67×#3113 | C2 | semidirect |
| 187. #3113 | D67 | semidirect |
| 193. C67 | #10044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571407 | 2 |
| #22570240 | 2 |
| #22558843 | 2 |
| #22558682 | 2 |
| #22558553 | 2 |
| #22558070 | 2 |
| C67×#3113 | 2 |
| #10044 | 67 |