Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
484 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22571154 | C2 | semidirect |
| 4. #22561181 | C2 | semidirect |
| 6. #22558053 | C2 | semidirect |
| 7. C67×#1518 | C2 | semidirect |
| 184. #1518 | D67 | semidirect |
| 187. C67 | #10223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571339 | 2 |
| #22571154 | 2 |
| #22570557 | 2 |
| #22561181 | 2 |
| #22558768 | 2 |
| #22558053 | 2 |
| C67×#1518 | 2 |
| #10223 | 67 |