Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
786 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 107 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. C71⋊#1304 | C2 | semidirect |
| 7. C2×#117×C71 | C4 | semidirect |
| 9. #379×C71 | C4 | semidirect |
| 103. C71 | #8749 | semidirect |
| 105. C2×#117 | Dic71 | semidirect |
| 109. #379 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588255 | 2 |
| C71⋊#1304 | 2 |
| C71×#2309 | 2 |
| #8749 | 71 |