Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
510 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 510 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 |
|---|---|---|
| 6. C22×Dic284 | C4 | semidirect |
| 12. C2×#14556062 | C4 | semidirect |
| 14. C2×#14556053 | C4 | semidirect |
| 171. C71 | #9784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986240 | 2 |
| #22589325 | 2 |
| #22588365 | 2 |
| #22586913 | 2 |
| C71×#1752 | 2 |
| #9784 | 71 |