Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
610 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 3. #22558091 | C2 | semidirect |
| 4. #22558090 | C2 | semidirect |
| 5. C67×#1295 | C2 | semidirect |
| 9. #16863451 | C4 | semidirect |
| 126. #1295 | D67 | semidirect |
| 127. C67 | #8031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863451 | 2 |
| #22562615 | 2 |
| #22558091 | 2 |
| #22558090 | 2 |
| C67×#1295 | 2 |
| #8031 | 67 |