Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 12. #17985721 | C4 | semidirect |
| 13. #17985721 | C4 | semidirect |
| 14. #17985720 | C4 | semidirect |
| 15. C8×C71⋊C8 | C4 | semidirect |
| 109. C71 | #8803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22586643 | 2 |
| #22586213 | 2 |
| #22586212 | 2 |
| #22586211 | 2 |
| #22586204 | 2 |
| C71×#1288 | 2 |
| #8803 | 71 |