Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
258 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. #22586251 | C2 | semidirect |
| 5. #22586210 | C2 | semidirect |
| 6. #22586202 | C2 | semidirect |
| 7. C71×#1570 | C2 | semidirect |
| 121. #1570 | D71 | semidirect |
| 128. C71 | #10647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22587060 | 2 |
| #22587033 | 2 |
| #22586810 | 2 |
| #22586251 | 2 |
| #22586210 | 2 |
| #22586202 | 2 |
| C71×#1570 | 2 |
| #10647 | 71 |