Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1238 conjugacy classes of subgroups; only the 384 normal subgroups are shown.
This group has 1238 conjugacy classes of subgroups — too many to draw. Only its 384 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. #22626824 | C2 | semidirect |
| 2. #22625171 | C2 | semidirect |
| 3. #22625162 | C2 | semidirect |
| 37. C2×#41×C73 | C8 | semidirect |
| 121. C73 | #17353 | semidirect |
| 136. C2×#41 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626824 | 2 |
| #22625171 | 2 |
| #22625162 | 2 |
| C2×#17989070 | 2 |
| #17353 | 73 |