Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22559960 | C2 | semidirect |
| 2. #22558972 | C2 | semidirect |
| 3. #22558820 | C2 | semidirect |
| 4. #22558717 | C2 | semidirect |
| 16. #500×C67 | C4 | semidirect |
| 17. #493×C67 | C4 | semidirect |
| 18. #486×C67 | C4 | semidirect |
| 143. C67 | #9764 | semidirect |
| 145. #500 | Dic67 | semidirect |
| 146. #493 | Dic67 | semidirect |
| 147. #486 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22559960 | 2 |
| #22558972 | 2 |
| #22558820 | 2 |
| #22558717 | 2 |
| C67×#3169 | 2 |
| #9764 | 67 |