Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
200 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 55 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. C2×#16863233 | C2 | semidirect |
| 2. C2×#16863229 | C2 | semidirect |
| 3. #22562297 | C2 | semidirect |
| 5. #22558408 | C2 | semidirect |
| 6. #22558388 | C2 | semidirect |
| 7. C67×#1416 | C2 | semidirect |
| 33. C67⋊C32 | D4 | semidirect |
| 101. #1416 | D67 | semidirect |
| 103. C67 | #13699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863233 | 2 |
| C2×#16863229 | 2 |
| #22562297 | 2 |
| #22562296 | 2 |
| #22558408 | 2 |
| #22558388 | 2 |
| C67×#1416 | 2 |
| #13699 | 67 |