Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
556 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22570756 | C2 | semidirect |
| 4. #22558889 | C2 | semidirect |
| 5. #22558664 | C2 | semidirect |
| 6. #22558045 | C2 | semidirect |
| 76. #11761612 | SD16 | semidirect |
| 180. C67 | #10161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570756 | 2 |
| C2×#16863742 | 2 |
| #22561050 | 2 |
| #22558889 | 2 |
| #22558664 | 2 |
| #22558045 | 2 |
| C67×#3208 | 2 |
| #10161 | 67 |