Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
274 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22562003 | C2 | semidirect |
| 5. #22558309 | C2 | semidirect |
| 6. #22558308 | C2 | semidirect |
| 7. C67×#1388 | C2 | semidirect |
| 137. #1388 | D67 | semidirect |
| 140. C67 | #13497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562003 | 2 |
| #22561838 | 2 |
| #22560265 | 2 |
| #22560256 | 2 |
| #22558309 | 2 |
| #22558308 | 2 |
| C67×#1388 | 2 |
| #13497 | 67 |