Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
392 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 3. #22558995 | C2 | semidirect |
| 4. #22558910 | C2 | semidirect |
| 5. #22558707 | C2 | semidirect |
| 7. C67×#1285 | C2 | semidirect |
| 190. #1285 | D67 | semidirect |
| 191. C67 | #10510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571214 | 2 |
| #22561141 | 2 |
| #22558995 | 2 |
| #22558910 | 2 |
| #22558707 | 2 |
| #22558562 | 2 |
| C67×#1285 | 2 |
| #10510 | 67 |