Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
312 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 4. #22589130 | C2 | semidirect |
| 5. #22586455 | C2 | semidirect |
| 6. #22586436 | C2 | semidirect |
| 7. C71×#2108 | C2 | semidirect |
| 15. #17985816 | C4 | semidirect |
| 16. #17985813 | C4 | semidirect |
| 143. #2108 | D71 | semidirect |
| 148. C71 | #13146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590090 | 2 |
| C2×#17985807 | 2 |
| #22589238 | 2 |
| #22589130 | 2 |
| #22586455 | 2 |
| #22586436 | 2 |
| C71×#2108 | 2 |
| #13146 | 71 |