Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
294 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 294 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 |
|---|---|---|
| 1. #22561991 | C2 | semidirect |
| 2. #22561983 | C2 | semidirect |
| 6. #22558298 | C2 | semidirect |
| 7. C67×#1833 | C2 | semidirect |
| 146. #1833 | D67 | semidirect |
| 148. C67 | #13525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561991 | 2 |
| #22561983 | 2 |
| #22561944 | 2 |
| C2×#16863202 | 2 |
| #22561107 | 2 |
| #22558298 | 2 |
| C67×#1833 | 2 |
| #13525 | 67 |