Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
474 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 11. #17986295 | C4 | semidirect |
| 12. #17986210 | C4 | semidirect |
| 101. C4×Dic71 | Q16 | semidirect |
| 186. C71 | #9236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598380 | 2 |
| #22590814 | 2 |
| #22589316 | 2 |
| #22586838 | 2 |
| #22586768 | 2 |
| #22586172 | 2 |
| C71×#1303 | 2 |
| #9236 | 71 |