Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 19. #17985814 | C4 | semidirect |
| 139. C71 | #12954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597207 | 2 |
| #22590112 | 2 |
| C2×#17985816 | 2 |
| C2×#17985814 | 2 |
| #22589131 | 2 |
| #22586425 | 2 |
| C71×#1389 | 2 |
| #12954 | 71 |