Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
392 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22561830 | C2 | semidirect |
| 2. #22560259 | C2 | semidirect |
| 3. #22558200 | C2 | semidirect |
| 9. #16863178 | C22 | semidirect |
| 10. C67⋊#338 | C22 | semidirect |
| 154. C67 | #11870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561830 | 2 |
| #22560259 | 2 |
| #22558200 | 2 |
| C67×#3058 | 2 |
| #11870 | 67 |