Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
200 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 71 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. C4×Dic536 | C2 | semidirect |
| 4. #22558409 | C2 | semidirect |
| 5. #22558391 | C2 | semidirect |
| 7. C67×#1397 | C2 | semidirect |
| 12. #16863235 | C4 | semidirect |
| 25. Dic536 | C2×C4 | semidirect |
| 36. C32×C67 | C2×C4 | semidirect |
| 92. #1397 | D67 | semidirect |
| 93. C67 | #13652 | semidirect |
| 122. C32 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863235 | 2 |
| C4×Dic536 | 2 |
| C4×D1072 | 2 |
| #22558409 | 2 |
| #22558391 | 2 |
| #22558388 | 2 |
| C67×#1397 | 2 |
| #13652 | 67 |