Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
582 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 124 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. #22625668 | C2 | semidirect |
| 4. #22624774 | C2 | semidirect |
| 6. C22×#11924036 | C4 | semidirect |
| 10. C2×#14556658 | C4 | semidirect |
| 11. C2×#14556648 | C4 | semidirect |
| 15. C2×C4×#10596833 | C4 | semidirect |
| 17. #17989433 | C4 | semidirect |
| 18. #17989431 | C4 | semidirect |
| 116. C22×D73 | #97 | semidirect |
| 137. C2×Dic73 | #97 | semidirect |
| 149. #10596833 | #99 | semidirect |
| 190. C73 | #8160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989614 | 2 |
| #22625668 | 2 |
| #22625169 | 2 |
| #22624774 | 2 |
| #22609718 | 2 |
| #8160 | 73 |