Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1074 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1074 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 |
|---|---|---|
| 2. C2×#16863683 | C2 | semidirect |
| 3. #22559352 | C2 | direct (N × H) |
| 4. C2×#16863145 | C2 | semidirect |
| 5. C2×#16863125 | C2 | semidirect |
| 6. C2×#494×C67 | C2 | semidirect |
| 15. #16863683 | C22 | semidirect |
| 19. #16863145 | C22 | semidirect |
| 20. #16863125 | C22 | semidirect |
| 25. #494×C67 | C22 | semidirect |
| 152. C2×C67 | #1634 | semidirect |
| 157. C2×#494 | D67 | semidirect |
| 162. C67 | C2×#1634 | semidirect |
| 174. #494 | C2×D67 | semidirect |
| 308. C2 | #22559352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864112 | 2 |
| C2×#16863683 | 2 |
| #22559352 | 2 |
| C2×#16863145 | 2 |
| C2×#16863125 | 2 |
| C2×#494×C67 | 2 |
| C2×#1634 | 67 |