Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
590 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22621056 | C2 | semidirect |
| 2. #22615104 | C2 | semidirect |
| 3. #22608617 | C2 | semidirect |
| 4. #22608426 | C2 | semidirect |
| 5. #22608322 | C2 | semidirect |
| 6. #22607832 | C2 | semidirect |
| 221. C73 | #10241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621056 | 2 |
| #22615104 | 2 |
| #22608617 | 2 |
| #22608426 | 2 |
| #22608322 | 2 |
| #22607832 | 2 |
| C73×#3036 | 2 |
| #10241 | 73 |