Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
300 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 3. #22562361 | C2 | semidirect |
| 4. #22559614 | C2 | semidirect |
| 6. #22558189 | C2 | semidirect |
| 7. C67×#1332 | C2 | semidirect |
| 133. #1332 | D67 | semidirect |
| 134. C67 | #12385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573219 | 2 |
| #22562433 | 2 |
| #22562361 | 2 |
| #22559614 | 2 |
| #22558254 | 2 |
| #22558189 | 2 |
| C67×#1332 | 2 |
| #12385 | 67 |