Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 124 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. C2×#17989473 | C2 | semidirect |
| 2. #22625478 | C2 | semidirect |
| 3. #22624887 | C2 | semidirect |
| 4. #22624885 | C2 | semidirect |
| 52. #135×C73 | C8 | semidirect |
| 153. C73 | #11591 | semidirect |
| 173. #135 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989473 | 2 |
| #22625478 | 2 |
| #22624887 | 2 |
| #22624885 | 2 |
| #135×Dic73 | 2 |
| #11591 | 73 |