Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
384 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 2. C4×#14523974 | C2 | semidirect |
| 3. #22558970 | C2 | semidirect |
| 6. #22558066 | C2 | semidirect |
| 7. C67×#1285 | C2 | semidirect |
| 9. #16863523 | C4 | semidirect |
| 10. #16863520 | C4 | semidirect |
| 11. #16863473 | C4 | semidirect |
| 13. #16863461 | C4 | semidirect |
| 185. #1285 | D67 | semidirect |
| 186. C67 | #8694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569178 | 2 |
| C4×#14523974 | 2 |
| #22558970 | 2 |
| #22558735 | 2 |
| #22558732 | 2 |
| #22558066 | 2 |
| C67×#1285 | 2 |
| #8694 | 67 |