Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
506 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 112 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. #22624919 | C2 | direct (N × H) |
| 15. #17988825 | C4 | semidirect |
| 17. C2×#14556525 | C4 | semidirect |
| 19. C22×Q16×C73 | C4 | semidirect |
| 42. #14556525 | C2×C4 | semidirect |
| 48. C2×Q16×C73 | C2×C4 | semidirect |
| 148. C2×C73 | #1348 | semidirect |
| 159. C73 | C2×#1348 | semidirect |
| 160. C22×Q16 | #64408 | semidirect |
| 180. C2×Q16 | C2×#64408 | semidirect |
| 305. C2 | #22624919 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989482 | 2 |
| C2×#17989461 | 2 |
| #22624919 | 2 |
| C2×#17988825 | 2 |
| C2×#1348 | 73 |