Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
512 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 4. #22608482 | C2 | semidirect |
| 5. #22608378 | C2 | semidirect |
| 6. #22607797 | C2 | semidirect |
| 7. C73×#3113 | C2 | semidirect |
| 197. #3113 | D73 | semidirect |
| 203. C73 | #10024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620320 | 2 |
| #22615791 | 2 |
| #22608554 | 2 |
| #22608482 | 2 |
| #22608378 | 2 |
| #22607797 | 2 |
| C73×#3113 | 2 |
| #10024 | 73 |