Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
380 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 3. #22608696 | C2 | semidirect |
| 5. #22608526 | C2 | semidirect |
| 6. #22607804 | C2 | semidirect |
| 7. C73×#1559 | C2 | semidirect |
| 184. #1559 | D73 | semidirect |
| 188. C73 | #10498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620930 | 2 |
| #22610778 | 2 |
| #22608696 | 2 |
| #22608530 | 2 |
| #22608526 | 2 |
| #22607804 | 2 |
| C73×#1559 | 2 |
| #10498 | 73 |