Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22561974 | C2 | semidirect |
| 5. #22560334 | C2 | semidirect |
| 6. #22558316 | C2 | semidirect |
| 7. C67×#1383 | C2 | semidirect |
| 11. #16863507 | C4 | semidirect |
| 12. #16863502 | C4 | semidirect |
| 157. #1383 | D67 | semidirect |
| 158. C67 | #12828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569092 | 2 |
| #22561974 | 2 |
| #22561946 | 2 |
| #22561936 | 2 |
| #22560334 | 2 |
| #22558316 | 2 |
| C67×#1383 | 2 |
| #12828 | 67 |