Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
924 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22571596 | C2 | semidirect |
| 2. #22570719 | C2 | semidirect |
| 3. #22559493 | C2 | semidirect |
| 4. #22559444 | C2 | semidirect |
| 5. #22558947 | C2 | semidirect |
| 6. #22558660 | C2 | semidirect |
| 170. C67 | #18701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571596 | 2 |
| #22570719 | 2 |
| #22559493 | 2 |
| #22559444 | 2 |
| #22558947 | 2 |
| #22558660 | 2 |
| C67×#3548 | 2 |
| #18701 | 67 |