Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22558859 | C2 | semidirect |
| 3. #22558703 | C2 | semidirect |
| 4. #22558040 | C2 | semidirect |
| 5. C67×#1940 | C2 | semidirect |
| 151. #1940 | D67 | semidirect |
| 155. C67 | #10546 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570655 | 2 |
| #22558859 | 2 |
| #22558703 | 2 |
| #22558040 | 2 |
| C67×#1940 | 2 |
| #10546 | 67 |