Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
490 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 81. #11761612 | Q16 | semidirect |
| 187. C67 | #10203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571551 | 2 |
| #22570751 | 2 |
| #22561154 | 2 |
| #22561133 | 2 |
| #22558709 | 2 |
| #22558058 | 2 |
| C67×#3230 | 2 |
| #10203 | 67 |