Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
298 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 144. C67 | #10644 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22560221 | 2 |
| #22560202 | 2 |
| #22558980 | 2 |
| #22558605 | 2 |
| #22558104 | 2 |
| #22558067 | 2 |
| C67×#1286 | 2 |
| #10644 | 67 |