Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
5294 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 5294 conjugacy classes of subgroups — too many to draw. Only its 827 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 |
|---|---|---|
| 1. C22×#14556109 | C2 | semidirect |
| 2. C2×#17986189 | C2 | direct (N × H) |
| 3. C22×#14556043 | C2 | semidirect |
| 5. C24×Dic71 | C22 | semidirect |
| 7. C2×#14556109 | C22 | semidirect |
| 10. C22×C22⋊Dic71 | C22 | semidirect |
| 11. #17986189 | C22 | direct (N × H) |
| 12. C2×#14556043 | C22 | semidirect |
| 21. C23×Dic71 | C23 | semidirect |
| 23. #14556109 | C23 | semidirect |
| 27. C2×C22⋊Dic71 | C23 | semidirect |
| 28. #14556043 | C23 | semidirect |
| 54. C22×Dic71 | C24 | semidirect |
| 58. C22⋊Dic71 | C24 | semidirect |
| 125. C22×C71 | #458 | semidirect |
| 136. C2×C71 | C2×#458 | semidirect |
| 142. C71 | C22×#458 | semidirect |
| 263. C22 | #17986189 | direct (N × H) |
| 273. C2 | C2×#17986189 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556109 | 2 |
| C2×#17986189 | 2 |
| C22×#14556043 | 2 |
| C22×H(5,𝔽2)×C71 | 2 |
| C22×#458 | 71 |