Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
396 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 119 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. #17985803 | C4 | semidirect |
| 143. C71 | #12957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985821 | 2 |
| C2×#17985815 | 2 |
| #22590060 | 2 |
| #22589093 | 2 |
| #22586447 | 2 |
| #22586420 | 2 |
| C2×#441×C71 | 2 |
| #12957 | 71 |