Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22618848 | C2 | semidirect |
| 2. #22611680 | C2 | semidirect |
| 3. C2×#17988400 | C2 | semidirect |
| 4. #22610842 | C2 | semidirect |
| 5. #22608043 | C2 | semidirect |
| 6. #22608018 | C2 | semidirect |
| 24. #509×C73 | C4 | semidirect |
| 179. C73 | #13032 | semidirect |
| 184. #509 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618848 | 2 |
| #22611680 | 2 |
| C2×#17988400 | 2 |
| #22610842 | 2 |
| #22608043 | 2 |
| #22608018 | 2 |
| C2×#509×C73 | 2 |
| #13032 | 73 |