Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22622943 | C2 | semidirect |
| 2. #22612194 | C2 | semidirect |
| 3. #22612192 | C2 | semidirect |
| 4. #22611992 | C2 | semidirect |
| 5. #22611986 | C2 | semidirect |
| 6. #22611965 | C2 | semidirect |
| 7. #22611839 | C2 | semidirect |
| 8. #22611794 | C2 | semidirect |
| 9. C4×D16×C73 | C2 | semidirect |
| 158. C4×D16 | D73 | semidirect |
| 159. C73 | #33970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622943 | 2 |
| #22612194 | 2 |
| #22612192 | 2 |
| #22611992 | 2 |
| #22611986 | 2 |
| #22611965 | 2 |
| #22611839 | 2 |
| #22611794 | 2 |
| C4×D16×C73 | 2 |
| #33970 | 73 |