Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
258 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 1. #22558980 | C2 | semidirect |
| 5. #22558119 | C2 | semidirect |
| 6. #22558078 | C2 | semidirect |
| 7. C67×#1287 | C2 | semidirect |
| 127. #1287 | D67 | semidirect |
| 128. C67 | #10647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22558980 | 2 |
| #22558932 | 2 |
| #22558905 | 2 |
| #22558679 | 2 |
| #22558119 | 2 |
| #22558078 | 2 |
| C67×#1287 | 2 |
| #10647 | 67 |