Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
404 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22558968 | C2 | semidirect |
| 4. C67⋊#1309 | C2 | semidirect |
| 5. C67×#1566 | C2 | semidirect |
| 138. #1566 | D67 | semidirect |
| 141. C67 | #8640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568922 | 2 |
| #22558968 | 2 |
| #22558942 | 2 |
| C67⋊#1309 | 2 |
| C67×#1566 | 2 |
| #8640 | 67 |