Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
412 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #22608255 | C2 | semidirect |
| 3. #22607864 | C2 | semidirect |
| 5. C73×#1467 | C2 | semidirect |
| 172. #1467 | D73 | semidirect |
| 176. C73 | #11565 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22614907 | 2 |
| #22608255 | 2 |
| #22607864 | 2 |
| #22607862 | 2 |
| C73×#1467 | 2 |
| #11565 | 73 |