Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
776 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 776 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 |
|---|---|---|
| 3. #22586360 | C2 | direct (N × H) |
| 5. C23×Dic142 | C4 | semidirect |
| 10. #17985911 | C4 | semidirect |
| 13. C2×C71⋊#95 | C4 | semidirect |
| 24. C22×Dic142 | C2×C4 | semidirect |
| 36. C71⋊#95 | C2×C4 | semidirect |
| 203. C2×C71 | #1351 | semidirect |
| 211. C71 | C2×#1351 | semidirect |
| 409. C2 | #22586360 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985911 | 2 |
| C2×#17985723 | 2 |
| #22586360 | 2 |
| C2×#342×C71 | 2 |
| C2×#1351 | 71 |