Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
574 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 574 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 |
|---|---|---|
| 1. #22571332 | C2 | semidirect |
| 3. #22561029 | C2 | semidirect |
| 4. #22558770 | C2 | semidirect |
| 5. C67×#1281 | C2 | semidirect |
| 132. #1281 | D67 | semidirect |
| 133. C67 | #10225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571332 | 2 |
| #22570655 | 2 |
| #22561029 | 2 |
| #22558770 | 2 |
| C67×#1281 | 2 |
| #10225 | 67 |