Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
15150 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 15150 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 |
|---|---|---|
| 2. C22×#14556111 | C2 | direct (N × H) |
| 3. C23×Dic71⋊C4 | C2 | semidirect |
| 4. C23×C22⋊Dic71 | C2 | semidirect |
| 5. C23×(C2×D71)⋊C4 | C2 | semidirect |
| 6. C25×C4×C71 | C2 | semidirect |
| 12. C2×#14556111 | C22 | direct (N × H) |
| 13. C22×Dic71⋊C4 | C22 | semidirect |
| 14. C22×C22⋊Dic71 | C22 | semidirect |
| 15. C22×(C2×D71)⋊C4 | C22 | semidirect |
| 19. C24×C4×C71 | C22 | semidirect |
| 29. #14556111 | C23 | direct (N × H) |
| 30. C2×Dic71⋊C4 | C23 | semidirect |
| 31. C2×C22⋊Dic71 | C23 | semidirect |
| 32. C2×(C2×D71)⋊C4 | C23 | semidirect |
| 40. C23×C4×C71 | C23 | semidirect |
| 51. Dic71⋊C4 | C24 | semidirect |
| 52. C22⋊Dic71 | C24 | semidirect |
| 53. (C2×D71)⋊C4 | C24 | semidirect |
| 64. C22×C4×C71 | C24 | semidirect |
| 67. C23×C71 | #123 | semidirect |
| 87. C22×C71 | C2×#123 | semidirect |
| 100. C2×C71 | C22×#123 | semidirect |
| 105. C25×C4 | D71 | semidirect |
| 110. C71 | C23×#123 | semidirect |
| 119. C24×C4 | C2×D71 | semidirect |
| 140. C23×C4 | C22×D71 | semidirect |
| 165. C22×C4 | C23×D71 | semidirect |
| 175. C23 | #14556111 | direct (N × H) |
| 194. C22 | C2×#14556111 | direct (N × H) |
| 204. C2 | C22×#14556111 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C22⋊D71 | 2 |
| C22×#14556111 | 2 |
| C23×Dic71⋊C4 | 2 |
| C23×C22⋊Dic71 | 2 |
| C23×(C2×D71)⋊C4 | 2 |
| C25×C4×C71 | 2 |
| C23×#123 | 71 |