Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
350 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 10. #17986126 | C4 | semidirect |
| 12. #17986123 | C4 | semidirect |
| 157. C71 | #8681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597270 | 2 |
| #22588470 | 2 |
| #22587086 | 2 |
| #22586905 | 2 |
| #22586903 | 2 |
| #22586200 | 2 |
| C71×#1286 | 2 |
| #8681 | 71 |