Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
292 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 14. #17985828 | C4 | semidirect |
| 15. #17985823 | C4 | semidirect |
| 16. #17985776 | C4 | semidirect |
| 116. C71 | #12678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590134 | 2 |
| #22590114 | 2 |
| C2×#17985776 | 2 |
| #22588248 | 2 |
| #22588227 | 2 |
| #22586455 | 2 |
| C71×#1388 | 2 |
| #12678 | 71 |