Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
306 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #22558265 | C2 | semidirect |
| 5. #22558263 | C2 | semidirect |
| 6. #22558258 | C2 | semidirect |
| 7. C67×#1362 | C2 | semidirect |
| 134. #1362 | D67 | semidirect |
| 135. C67 | #11984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570793 | 2 |
| C4⋊C16×D67 | 2 |
| #22558971 | 2 |
| #22558265 | 2 |
| #22558263 | 2 |
| #22558258 | 2 |
| C67×#1362 | 2 |
| #11984 | 67 |