Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
866 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 251 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×#17988985 | C2 | semidirect |
| 2. C2×#17988939 | C2 | semidirect |
| 4. #22609530 | C2 | direct (N × H) |
| 5. C2×C8×#10596831 | C2 | semidirect |
| 9. #17988985 | C22 | semidirect |
| 11. #17988939 | C22 | semidirect |
| 18. C8×#10596831 | C22 | semidirect |
| 123. C2×C73 | #1708 | semidirect |
| 132. C73 | C2×#1708 | semidirect |
| 248. C2 | #22609530 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988985 | 2 |
| C2×#17988939 | 2 |
| C2×#17988933 | 2 |
| #22609530 | 2 |
| C2×C8×#10596831 | 2 |
| C2×#492×C73 | 2 |
| C2×#1708 | 73 |