Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
294 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 21. C4⋊#11924003 | C4 | semidirect |
| 22. #17988405 | C4 | semidirect |
| 23. #17988405 | C4 | semidirect |
| 24. C4⋊C16×C73 | C4 | semidirect |
| 145. C73 | #13184 | semidirect |
| 161. C4⋊C16 | #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 |
| #22625868 | 2 |
| C4×#14556661 | 2 |
| #22624996 | 2 |
| #22611685 | 2 |
| #13184 | 73 |