Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 4. #22607999 | C2 | semidirect |
| 5. #22607992 | C2 | semidirect |
| 6. #22607970 | C2 | semidirect |
| 7. C73×#2245 | C2 | semidirect |
| 93. #2245 | D73 | semidirect |
| 100. C73 | #12466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612104 | 2 |
| #22612009 | 2 |
| #22611774 | 2 |
| #22607999 | 2 |
| #22607992 | 2 |
| #22607970 | 2 |
| C73×#2245 | 2 |
| #12466 | 73 |