Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
186 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22590635 | C2 | semidirect |
| 2. #22590634 | C2 | semidirect |
| 4. #22586537 | C2 | semidirect |
| 5. #22586481 | C2 | semidirect |
| 6. C32×Dic71 | C2 | semidirect |
| 7. C71×#1401 | C2 | semidirect |
| 97. #1401 | D71 | semidirect |
| 99. C71 | #13647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590635 | 2 |
| #22590634 | 2 |
| #22590175 | 2 |
| #22586537 | 2 |
| #22586481 | 2 |
| C32×Dic71 | 2 |
| C71×#1401 | 2 |
| #13647 | 71 |