Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
518 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
|---|---|---|
| 11. #17985720 | C4 | semidirect |
| 12. C8×C71⋊C8 | C4 | semidirect |
| 15. #322×C71 | C4 | semidirect |
| 77. C71 | #7844 | semidirect |
| 86. #322 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588085 | 2 |
| C4×#14556038 | 2 |
| C2×#17985720 | 2 |
| C2×C8×C71⋊C8 | 2 |
| C2×#322×C71 | 2 |
| #7844 | 71 |