Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
396 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
| 2. C2×#17989511 | C2 | semidirect |
| 5. #22624996 | C2 | semidirect |
| 6. #22624996 | C2 | semidirect |
| 19. C2×#14556531 | C4 | semidirect |
| 24. C2×C16×D73 | C4 | semidirect |
| 25. C2×C16×D73 | C4 | semidirect |
| 26. C2×M32×C73 | C4 | semidirect |
| 104. #11924003 | C22⋊C4 | semidirect |
| 111. C16×C73 | C22⋊C4 | semidirect |
| 161. C2×D73 | #365 | semidirect |
| 187. C73 | #12831 | semidirect |
| 194. C2×M32 | #64408 | semidirect |
| 291. C16 | C22⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989512 | 2 |
| C2×#17989511 | 2 |
| #22625810 | 2 |
| #22625807 | 2 |
| #22624996 | 2 |
| C2×M32×D73 | 2 |
| #12831 | 73 |