Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
356 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 2. #22612009 | C2 | semidirect |
| 3. #22609547 | C2 | semidirect |
| 4. #22607969 | C2 | semidirect |
| 5. #22607904 | C2 | semidirect |
| 6. #22607903 | C2 | semidirect |
| 7. C73×#2214 | C2 | semidirect |
| 143. #2214 | D73 | semidirect |
| 148. C73 | #12313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621736 | 2 |
| #22612009 | 2 |
| #22609547 | 2 |
| #22607969 | 2 |
| #22607904 | 2 |
| #22607903 | 2 |
| C73×#2214 | 2 |
| #12313 | 73 |