Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
216 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 15. #17988309 | C4 | semidirect |
| 16. #17988309 | C4 | semidirect |
| 17. C8×#10596831 | C4 | semidirect |
| 18. #322×C73 | C4 | semidirect |
| 109. C73 | #8803 | semidirect |
| 119. #322 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22624798 | 2 |
| #22624791 | 2 |
| #22608235 | 2 |
| #8803 | 73 |