Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
572 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22565697 | C2 | semidirect |
| 3. #22561129 | C2 | semidirect |
| 4. #22558808 | C2 | semidirect |
| 5. #22558656 | C2 | semidirect |
| 6. #22558064 | C2 | semidirect |
| 7. C67×#3112 | C2 | semidirect |
| 218. #3112 | D67 | semidirect |
| 224. C67 | #10006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571192 | 2 |
| #22565697 | 2 |
| #22561129 | 2 |
| #22558808 | 2 |
| #22558656 | 2 |
| #22558064 | 2 |
| C67×#3112 | 2 |
| #10006 | 67 |