Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
282 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22562244 | C2 | semidirect |
| 2. #22559823 | C2 | semidirect |
| 3. #22559094 | C2 | semidirect |
| 4. #22558272 | C2 | semidirect |
| 5. #22558256 | C2 | semidirect |
| 6. #22558255 | C2 | semidirect |
| 7. C67×#2206 | C2 | semidirect |
| 104. C67⋊C8 | D16 | semidirect |
| 129. #2206 | D67 | semidirect |
| 135. C67 | #12491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562244 | 2 |
| #22559823 | 2 |
| #22559094 | 2 |
| #22558272 | 2 |
| #22558256 | 2 |
| #22558255 | 2 |
| C67×#2206 | 2 |
| #12491 | 67 |