Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 149 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. #22560369 | C2 | semidirect |
| 4. #22560337 | C2 | semidirect |
| 5. C67×#1273 | C2 | semidirect |
| 113. #1273 | D67 | semidirect |
| 114. C67 | #10671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561015 | 2 |
| #22560369 | 2 |
| #22560337 | 2 |
| C67×#1273 | 2 |
| #10671 | 67 |