Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
438 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 76 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. #22626756 | C2 | semidirect |
| 2. #22625407 | C2 | semidirect |
| 3. C2×#17989443 | C2 | semidirect |
| 4. #22625202 | C2 | semidirect |
| 5. #22624826 | C2 | semidirect |
| 6. #22624770 | C2 | semidirect |
| 220. C73 | #9265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626756 | 2 |
| #22625407 | 2 |
| C2×#17989443 | 2 |
| #22625202 | 2 |
| #22624826 | 2 |
| #22624770 | 2 |
| #22620895 | 2 |
| #9265 | 73 |