Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
474 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22560677 | C2 | semidirect |
| 4. #22558728 | C2 | semidirect |
| 6. #22558086 | C2 | semidirect |
| 7. C67×#1851 | C2 | semidirect |
| 225. #1851 | D67 | semidirect |
| 229. C67 | #10558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570967 | 2 |
| #22560677 | 2 |
| #22560672 | 2 |
| #22558728 | 2 |
| #22558724 | 2 |
| #22558086 | 2 |
| C67×#1851 | 2 |
| #10558 | 67 |