Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
386 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22610084 | C2 | semidirect |
| 2. #22608631 | C2 | semidirect |
| 4. #22608443 | C2 | semidirect |
| 6. #22607801 | C2 | semidirect |
| 165. C73 | #10514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610084 | 2 |
| #22608631 | 2 |
| #22608626 | 2 |
| #22608443 | 2 |
| #22608439 | 2 |
| #22607801 | 2 |
| C73×#3246 | 2 |
| #10514 | 73 |