Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
440 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22561881 | C2 | semidirect |
| 3. #22561860 | C2 | semidirect |
| 4. #22560736 | C2 | semidirect |
| 5. #22560495 | C2 | semidirect |
| 6. #22558339 | C2 | semidirect |
| 7. C67×#1914 | C2 | semidirect |
| 205. #1914 | D67 | semidirect |
| 209. C67 | #13432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571070 | 2 |
| #22561881 | 2 |
| #22561860 | 2 |
| #22560736 | 2 |
| #22560495 | 2 |
| #22558339 | 2 |
| C67×#1914 | 2 |
| #13432 | 67 |