Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
320 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 82 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. #22626289 | C2 | semidirect |
| 2. C2×#17989450 | C2 | semidirect |
| 3. #22624887 | C2 | semidirect |
| 4. #22624886 | C2 | semidirect |
| 146. C73 | #11648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626289 | 2 |
| C2×#17989450 | 2 |
| #22624887 | 2 |
| #22624886 | 2 |
| #22620502 | 2 |
| #11648 | 73 |