Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
914 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 251 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×#16863799 | C2 | semidirect |
| 4. #22559881 | C2 | direct (N × H) |
| 5. C2×#16863117 | C2 | semidirect |
| 6. C2×#494×C67 | C2 | semidirect |
| 11. #16863799 | C22 | semidirect |
| 19. #16863117 | C22 | semidirect |
| 23. #494×C67 | C22 | semidirect |
| 124. C2×C67 | #1722 | semidirect |
| 129. C2×#494 | D67 | semidirect |
| 134. C67 | C2×#1722 | semidirect |
| 143. #494 | C2×D67 | semidirect |
| 252. C2 | #22559881 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863799 | 2 |
| C2×#16863769 | 2 |
| C2×#16863744 | 2 |
| #22559881 | 2 |
| C2×#16863117 | 2 |
| C2×#494×C67 | 2 |
| C2×#1722 | 67 |