Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
286 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22611743 | C2 | semidirect |
| 2. #22610080 | C2 | semidirect |
| 3. #22607925 | C2 | semidirect |
| 5. #22607919 | C2 | semidirect |
| 17. #499×C73 | C4 | semidirect |
| 18. #495×C73 | C4 | semidirect |
| 23. #442×C73 | C4 | semidirect |
| 24. #441×C73 | C4 | semidirect |
| 147. C73 | #11836 | semidirect |
| 149. #499 | Dic73 | semidirect |
| 150. #495 | Dic73 | semidirect |
| 155. #442 | Dic73 | semidirect |
| 156. #441 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611743 | 2 |
| #22610080 | 2 |
| #22607925 | 2 |
| #22607922 | 2 |
| #22607919 | 2 |
| #22607916 | 2 |
| C73×#3183 | 2 |
| #11836 | 73 |