Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
474 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#17988693 | C2 | semidirect |
| 3. C2×#17988404 | C2 | semidirect |
| 5. #22608029 | C2 | semidirect |
| 6. #22608010 | C2 | semidirect |
| 12. C2×#14556537 | C4 | semidirect |
| 13. C2×#14556535 | C4 | semidirect |
| 177. C73 | #13038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989027 | 2 |
| C2×#17988693 | 2 |
| C2×#17988404 | 2 |
| #22610825 | 2 |
| #22608029 | 2 |
| #22608010 | 2 |
| C2×#360×C73 | 2 |
| #13038 | 73 |