Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22611704 | C2 | semidirect |
| 2. #22611659 | C2 | semidirect |
| 3. #22611647 | C2 | semidirect |
| 4. #22611535 | C2 | semidirect |
| 5. #22610842 | C2 | semidirect |
| 6. #22610830 | C2 | semidirect |
| 24. C2×SD32×C73 | C4 | semidirect |
| 25. C2×D16×C73 | C4 | semidirect |
| 175. C73 | #13247 | semidirect |
| 180. C2×SD32 | Dic73 | semidirect |
| 181. C2×D16 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611704 | 2 |
| #22611659 | 2 |
| #22611647 | 2 |
| #22611535 | 2 |
| #22610842 | 2 |
| #22610830 | 2 |
| C2×#509×C73 | 2 |
| #13247 | 73 |