Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
186 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22612226 | C2 | semidirect |
| 2. #22612225 | C2 | semidirect |
| 4. #22608128 | C2 | semidirect |
| 5. #22608072 | C2 | semidirect |
| 6. C32×Dic73 | C2 | semidirect |
| 7. C73×#1401 | C2 | semidirect |
| 97. #1401 | D73 | semidirect |
| 99. C73 | #13647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612226 | 2 |
| #22612225 | 2 |
| #22611766 | 2 |
| #22608128 | 2 |
| #22608072 | 2 |
| C32×Dic73 | 2 |
| C73×#1401 | 2 |
| #13647 | 73 |