Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
474 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 474 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 |
|---|---|---|
| 3. #22588523 | C2 | semidirect |
| 4. #22586860 | C2 | semidirect |
| 6. #22586216 | C2 | semidirect |
| 7. C71×#1901 | C2 | semidirect |
| 223. #1901 | D71 | semidirect |
| 229. C71 | #10558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599093 | 2 |
| #22588803 | 2 |
| #22588523 | 2 |
| #22586860 | 2 |
| #22586857 | 2 |
| #22586216 | 2 |
| C71×#1901 | 2 |
| #10558 | 71 |