Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
686 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 203 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×#16863798 | C2 | semidirect |
| 3. #22562451 | C2 | direct (N × H) |
| 4. C2×#16863198 | C2 | semidirect |
| 5. C2×#346×C67 | C2 | semidirect |
| 11. #16863798 | C22 | semidirect |
| 16. #16863198 | C22 | semidirect |
| 19. #346×C67 | C22 | semidirect |
| 98. C2×C67 | #2244 | semidirect |
| 106. C2×#346 | D67 | semidirect |
| 107. C67 | C2×#2244 | semidirect |
| 121. #346 | C2×D67 | semidirect |
| 200. C2 | #22562451 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863798 | 2 |
| C2×#16863773 | 2 |
| #22562451 | 2 |
| C2×#16863198 | 2 |
| C2×#346×C67 | 2 |
| C2×#2244 | 67 |