Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
14334 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 14334 conjugacy classes of subgroups — too many to draw. Only its 4427 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. C24×Dic142 | C2 | semidirect |
| 2. C22×#14556115 | C2 | direct (N × H) |
| 3. C23×C22⋊Dic71 | C2 | semidirect |
| 4. C23×C4×Dic71 | C2 | semidirect |
| 7. C23×Dic142 | C22 | semidirect |
| 10. C2×#14556115 | C22 | direct (N × H) |
| 11. C22×C22⋊Dic71 | C22 | semidirect |
| 12. C22×C4×Dic71 | C22 | semidirect |
| 18. C22×Dic142 | C23 | semidirect |
| 23. #14556115 | C23 | direct (N × H) |
| 24. C2×C22⋊Dic71 | C23 | semidirect |
| 25. C2×C4×Dic71 | C23 | semidirect |
| 35. C2×Dic142 | C24 | semidirect |
| 40. C22⋊Dic71 | C24 | semidirect |
| 41. C4×Dic71 | C24 | semidirect |
| 56. C23×C71 | #124 | semidirect |
| 72. C22×C71 | C2×#124 | semidirect |
| 81. C2×C71 | C22×#124 | semidirect |
| 89. C71 | C23×#124 | semidirect |
| 140. C23 | #14556115 | direct (N × H) |
| 156. C22 | C2×#14556115 | direct (N × H) |
| 164. C2 | C22×#14556115 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic142 | 2 |
| C22×#14556115 | 2 |
| C23×C22⋊Dic71 | 2 |
| C23×C4×Dic71 | 2 |
| C24×D4×C71 | 2 |
| C23×#124 | 71 |