Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1050 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 227 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. #22562934 | C2 | semidirect |
| 3. #22561033 | C2 | semidirect |
| 4. #22560556 | C2 | semidirect |
| 5. #22560340 | C2 | semidirect |
| 6. C67×#1746 | C2 | semidirect |
| 10. #16863773 | C4 | semidirect |
| 24. C2×D536 | C2×C4 | semidirect |
| 26. #14524040 | C2×C4 | semidirect |
| 38. C4×C8×C67 | C2×C4 | semidirect |
| 108. #1746 | D67 | semidirect |
| 109. C67 | #22276 | semidirect |
| 140. C4×C8 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863773 | 2 |
| #22562934 | 2 |
| #22561033 | 2 |
| #22560556 | 2 |
| #22560340 | 2 |
| C67×#1746 | 2 |
| #22276 | 67 |