Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 1. C2×#17989509 | C2 | semidirect |
| 2. C2×C8×#10596833 | C2 | semidirect |
| 3. #22624894 | C2 | direct (N × H) |
| 8. #17989509 | C22 | semidirect |
| 10. C8×#10596833 | C22 | semidirect |
| 29. #14556613 | C8 | semidirect |
| 31. C2×Dic292 | C8 | semidirect |
| 33. C2×D584 | C8 | semidirect |
| 65. Dic292 | C2×C8 | semidirect |
| 69. D584 | C2×C8 | semidirect |
| 139. C2×C73 | #1335 | semidirect |
| 146. C73 | C2×#1335 | semidirect |
| 281. C2 | #22624894 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989509 | 2 |
| C2×C8×#10596833 | 2 |
| #22624894 | 2 |
| C2×#17988703 | 2 |
| C2×#1335 | 73 |