Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1206 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 403 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. #22562571 | C2 | semidirect |
| 3. C4×#14523977 | C2 | semidirect |
| 4. #22560035 | C2 | semidirect |
| 5. C67×#1726 | C2 | semidirect |
| 8. C4×D536 | C4 | semidirect |
| 22. C4×D268 | C2×C4 | semidirect |
| 26. #14523977 | C2×C4 | semidirect |
| 27. #14523965 | C2×C4 | semidirect |
| 33. C4×C8×C67 | C2×C4 | semidirect |
| 42. D536 | C42 | semidirect |
| 93. #1726 | D67 | semidirect |
| 94. C67 | #20508 | semidirect |
| 121. 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×C4×D536 | 2 |
| #22562571 | 2 |
| C4×#14523977 | 2 |
| #22560035 | 2 |
| C67×#1726 | 2 |
| #20508 | 67 |