Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
542 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22613117 | C2 | semidirect |
| 3. C2×#17988329 | C2 | semidirect |
| 4. #22607813 | C2 | semidirect |
| 17. #490×C73 | C4 | semidirect |
| 141. C73 | #9002 | semidirect |
| 145. #490 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22613117 | 2 |
| #22610756 | 2 |
| C2×#17988329 | 2 |
| #22607813 | 2 |
| C2×#490×C73 | 2 |
| #9002 | 73 |