Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
610 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22570145 | C2 | semidirect |
| 2. #22565999 | C2 | semidirect |
| 3. #22561046 | C2 | semidirect |
| 4. #22560306 | C2 | semidirect |
| 5. #22558725 | C2 | semidirect |
| 6. #22558114 | C2 | semidirect |
| 243. C67 | #9932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570145 | 2 |
| #22565999 | 2 |
| #22561046 | 2 |
| #22560306 | 2 |
| #22558725 | 2 |
| #22558114 | 2 |
| C67×#3192 | 2 |
| #9932 | 67 |