Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
394 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 2. #22587131 | C2 | semidirect |
| 4. #22587021 | C2 | semidirect |
| 6. #22586230 | C2 | semidirect |
| 7. C71×#1966 | C2 | semidirect |
| 160. #1966 | D71 | semidirect |
| 166. C71 | #10489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599265 | 2 |
| #22587131 | 2 |
| #22587073 | 2 |
| #22587021 | 2 |
| #22586758 | 2 |
| #22586230 | 2 |
| C71×#1966 | 2 |
| #10489 | 71 |