Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
738 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 135 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. #22609867 | C2 | semidirect |
| 4. #22607799 | C2 | semidirect |
| 10. #17988507 | C4 | semidirect |
| 11. #17988499 | C4 | semidirect |
| 110. C23×C73 | #103 | semidirect |
| 130. C2×C4×C73 | #103 | semidirect |
| 189. C73 | #9467 | semidirect |
| 294. C23 | #14556516 | semidirect |
| 328. C2×C4 | #14556516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22613296 | 2 |
| #22609919 | 2 |
| #22609867 | 2 |
| #22607799 | 2 |
| C73×#2972 | 2 |
| #9467 | 73 |