Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22612172 | C2 | semidirect |
| 2. #22612107 | C2 | semidirect |
| 3. #22611773 | C2 | semidirect |
| 4. #22607998 | C2 | semidirect |
| 5. #22607991 | C2 | semidirect |
| 6. #22607968 | C2 | semidirect |
| 103. C73 | #12465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612172 | 2 |
| #22612107 | 2 |
| #22611773 | 2 |
| #22607998 | 2 |
| #22607991 | 2 |
| #22607968 | 2 |
| C73×#2213 | 2 |
| #12465 | 73 |