Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1004 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22574623 | C2 | semidirect |
| 2. #22571150 | C2 | semidirect |
| 3. #22559285 | C2 | semidirect |
| 4. #22559266 | C2 | semidirect |
| 5. #22558871 | C2 | semidirect |
| 6. #22558631 | C2 | semidirect |
| 9. #16864132 | C22 | semidirect |
| 10. #16864126 | C22 | semidirect |
| 21. #16863145 | C22 | semidirect |
| 22. #16863140 | C22 | semidirect |
| 23. #16863128 | C22 | semidirect |
| 175. C67 | #18718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574623 | 2 |
| #22571150 | 2 |
| #22559285 | 2 |
| #22559266 | 2 |
| #22558871 | 2 |
| #22558631 | 2 |
| C67×#3151 | 2 |
| #18718 | 67 |