Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1072 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. #22620480 | C2 | semidirect |
| 3. #22619749 | C2 | semidirect |
| 4. #22611141 | C2 | semidirect |
| 5. #22610912 | C2 | semidirect |
| 6. #22610772 | C2 | semidirect |
| 7. #22610140 | C2 | semidirect |
| 8. #22609742 | C2 | semidirect |
| 9. C73×#2641 | C2 | semidirect |
| 102. #11924012 | #41 | semidirect |
| 203. #2641 | D73 | semidirect |
| 209. C73 | #25690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623805 | 2 |
| #22620480 | 2 |
| #22619749 | 2 |
| #22611141 | 2 |
| #22610912 | 2 |
| #22610772 | 2 |
| #22610140 | 2 |
| #22609742 | 2 |
| C73×#2641 | 2 |
| #25690 | 73 |