Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
304 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 1. #22590113 | C2 | semidirect |
| 5. #22589130 | C2 | semidirect |
| 6. #22586436 | C2 | semidirect |
| 7. C71×#2151 | C2 | semidirect |
| 138. #2151 | D71 | semidirect |
| 144. C71 | #13468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590113 | 2 |
| #22590069 | 2 |
| C2×#17985807 | 2 |
| #22589238 | 2 |
| #22589130 | 2 |
| #22586436 | 2 |
| C71×#2151 | 2 |
| #13468 | 71 |