Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
424 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 21. #16863194 | C4 | semidirect |
| 195. C67 | #12971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22563388 | 2 |
| C2×#16863194 | 2 |
| #22560600 | 2 |
| #22560426 | 2 |
| #22560423 | 2 |
| #22558335 | 2 |
| C67×#1394 | 2 |
| #12971 | 67 |