Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
458 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. C2×#17988403 | C2 | semidirect |
| 5. #22608039 | C2 | semidirect |
| 6. #22608025 | C2 | semidirect |
| 7. C2×#358×C73 | C2 | semidirect |
| 16. #17988859 | C4 | semidirect |
| 174. C2×#358 | D73 | semidirect |
| 178. C73 | #13072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989003 | 2 |
| C2×#17988859 | 2 |
| C2×#17988403 | 2 |
| #22609996 | 2 |
| #22608039 | 2 |
| #22608025 | 2 |
| C2×#358×C73 | 2 |
| #13072 | 73 |