Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
5838 conjugacy classes of subgroups; only the 1339 normal subgroups are shown.
This group has 5838 conjugacy classes of subgroups — too many to draw. Only its 1339 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. C23×Dic71⋊C4 | C2 | semidirect |
| 3. C2×#17985923 | C2 | direct (N × H) |
| 4. C22×#95×C71 | C2 | semidirect |
| 8. C22×Dic71⋊C4 | C22 | semidirect |
| 11. #17985923 | C22 | direct (N × H) |
| 13. C2×#95×C71 | C22 | semidirect |
| 23. C2×Dic71⋊C4 | C23 | semidirect |
| 31. #95×C71 | C23 | semidirect |
| 77. C22×C71 | #396 | semidirect |
| 91. C2×C71 | C2×#396 | semidirect |
| 99. C22×#95 | D71 | semidirect |
| 100. C71 | C22×#396 | semidirect |
| 109. C2×#95 | C2×D71 | semidirect |
| 127. #95 | C22×D71 | semidirect |
| 177. C22 | #17985923 | direct (N × H) |
| 187. C2 | C2×#17985923 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic71⋊C4 | 2 |
| C23×(C2×D71)⋊C4 | 2 |
| C2×#17985923 | 2 |
| C22×#95×C71 | 2 |
| C22×#396 | 71 |