Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
632 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 274 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 |
|---|---|---|
| 37. #125×C73 | C8 | semidirect |
| 116. C73 | #23369 | semidirect |
| 134. #125 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626028 | 2 |
| #22625984 | 2 |
| #22625846 | 2 |
| #125×Dic73 | 2 |
| #23369 | 73 |