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 |
|---|---|---|
| 2. #22588806 | C2 | semidirect |
| 4. #22588522 | C2 | semidirect |
| 5. #22586861 | C2 | semidirect |
| 7. C71×#1293 | C2 | semidirect |
| 228. #1293 | 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 |
|---|---|
| #22599098 | 2 |
| #22588806 | 2 |
| #22588801 | 2 |
| #22588522 | 2 |
| #22586861 | 2 |
| #22586857 | 2 |
| C71×#1293 | 2 |
| #10558 | 71 |