Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
676 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 115 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×#17988386 | C2 | semidirect |
| 4. #22608058 | C2 | semidirect |
| 200. C22×C73 | #356 | semidirect |
| 228. C73 | #13094 | semidirect |
| 423. C22 | #17988386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556510 | 2 |
| C2×#17988386 | 2 |
| #22609855 | 2 |
| #22608058 | 2 |
| C73×#2434 | 2 |
| #13094 | 73 |