Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
346 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22588480 | C2 | semidirect |
| 5. #22586198 | C2 | semidirect |
| 6. #22586184 | C2 | semidirect |
| 7. C71×#1286 | C2 | semidirect |
| 153. #1286 | D71 | semidirect |
| 155. C71 | #10634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589163 | 2 |
| #22588480 | 2 |
| #22587009 | 2 |
| #22587007 | 2 |
| #22586198 | 2 |
| #22586184 | 2 |
| C71×#1286 | 2 |
| #10634 | 71 |