Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
558 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22618649 | C2 | semidirect |
| 3. #22610754 | C2 | semidirect |
| 4. #22608598 | C2 | semidirect |
| 5. #22607789 | C2 | semidirect |
| 6. #22607761 | C2 | semidirect |
| 7. C73×#1517 | C2 | semidirect |
| 10. #17988963 | C4 | semidirect |
| 11. #17988935 | C4 | semidirect |
| 93. C2×#10596831 | D8 | semidirect |
| 200. #1517 | D73 | semidirect |
| 203. C73 | #9293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620846 | 2 |
| #22618649 | 2 |
| #22610754 | 2 |
| #22608598 | 2 |
| #22607789 | 2 |
| #22607761 | 2 |
| C73×#1517 | 2 |
| #9293 | 73 |