Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
394 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 139 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×#17988416 | C2 | semidirect |
| 4. #22608024 | C2 | semidirect |
| 85. C22×C73 | #368 | semidirect |
| 102. C73 | #12837 | semidirect |
| 182. C22 | #17988416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11924003 | 2 |
| C2×#17988416 | 2 |
| #22609969 | 2 |
| #22608024 | 2 |
| C73×#1810 | 2 |
| #12837 | 73 |