Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
366 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22588459 | C2 | semidirect |
| 4. #22586852 | C2 | semidirect |
| 6. #22586209 | C2 | semidirect |
| 7. C71×#1552 | C2 | semidirect |
| 159. #1552 | D71 | semidirect |
| 164. C71 | #10515 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599652 | 2 |
| #22588459 | 2 |
| #22587033 | 2 |
| #22586852 | 2 |
| #22586849 | 2 |
| #22586209 | 2 |
| C71×#1552 | 2 |
| #10515 | 71 |