Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22611705 | C2 | semidirect |
| 2. #22611647 | C2 | semidirect |
| 3. #22611647 | C2 | semidirect |
| 4. #22611559 | C2 | semidirect |
| 5. #22609977 | C2 | semidirect |
| 6. #22608045 | C2 | semidirect |
| 172. C73 | #13404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611705 | 2 |
| #22611647 | 2 |
| #22611559 | 2 |
| #22609977 | 2 |
| #22608045 | 2 |
| C2×#472×C73 | 2 |
| #13404 | 73 |