Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
356 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 22. #16863143 | C4 | semidirect |
| 23. #16863143 | C4 | semidirect |
| 24. #16863141 | C4 | semidirect |
| 25. #16863141 | C4 | semidirect |
| 157. C67 | #8936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569310 | 2 |
| #22561186 | 2 |
| #22558998 | 2 |
| #22558997 | 2 |
| #22558873 | 2 |
| #22558042 | 2 |
| C67×#1276 | 2 |
| #8936 | 67 |