Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
192 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 7. #17985777 | C4 | semidirect |
| 9. #17985720 | C4 | semidirect |
| 10. C8×C71⋊C8 | C4 | semidirect |
| 83. C71 | #7225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590152 | 2 |
| #22586643 | 2 |
| C71×#1841 | 2 |
| #7225 | 71 |