Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
936 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 155 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×#17989337 | C2 | semidirect |
| 2. #22621117 | C2 | semidirect |
| 3. #22609240 | C2 | semidirect |
| 4. #22609227 | C2 | semidirect |
| 5. #22608555 | C2 | semidirect |
| 6. #22608532 | C2 | semidirect |
| 16. #17988993 | C22 | semidirect |
| 17. #17988951 | C22 | semidirect |
| 22. #17988328 | C22 | semidirect |
| 194. C73 | #18994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989337 | 2 |
| #22621117 | 2 |
| #22609240 | 2 |
| #22609227 | 2 |
| #22608555 | 2 |
| #22608532 | 2 |
| C73×#3153 | 2 |
| #18994 | 73 |