Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
274 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 17. #17988417 | C4 | semidirect |
| 18. #17988416 | C4 | semidirect |
| 19. #368×C73 | C4 | semidirect |
| 105. C73 | #13172 | semidirect |
| 114. #368 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989514 | 2 |
| #22626139 | 2 |
| #22626049 | 2 |
| #22625007 | 2 |
| #368×D73 | 2 |
| #13172 | 73 |