Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
396 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 1. C2×#17989512 | C2 | semidirect |
| 4. #22624996 | C2 | semidirect |
| 15. C2×#14556530 | C4 | semidirect |
| 16. C2×#14556530 | C4 | semidirect |
| 19. C22×#11924003 | C4 | semidirect |
| 20. C22×C16×C73 | C4 | semidirect |
| 75. #11924003 | C22⋊C4 | semidirect |
| 82. C16×C73 | C22⋊C4 | semidirect |
| 113. C22×C73 | #365 | semidirect |
| 140. C73 | #12831 | semidirect |
| 148. C22×C16 | #64408 | semidirect |
| 217. C16 | C22⋊#64408 | semidirect |
| 255. C22 | #17989512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989512 | 2 |
| #22625810 | 2 |
| #22625807 | 2 |
| #22624996 | 2 |
| C22×#14556530 | 2 |
| #12831 | 73 |