Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
184 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. #22586520 | C2 | semidirect |
| 4. #22586474 | C2 | semidirect |
| 5. C71×#2252 | C2 | semidirect |
| 75. #2252 | D71 | semidirect |
| 80. C71 | #13722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590601 | 2 |
| #22586520 | 2 |
| #22586517 | 2 |
| #22586474 | 2 |
| C71×#2252 | 2 |
| #13722 | 71 |