Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
180 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22558284 | C2 | semidirect |
| 4. #22558277 | C2 | semidirect |
| 5. C67×#1369 | C2 | semidirect |
| 78. #1369 | D67 | semidirect |
| 79. C67 | #12026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562024 | 2 |
| #22561807 | 2 |
| #22558284 | 2 |
| #22558277 | 2 |
| C67×#1369 | 2 |
| #12026 | 67 |