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 |
| 3. C22×#14556116 | C2 | direct (N × H) |
| 4. C23×(C2×D71)⋊C4 | C2 | semidirect |
| 5. C23×C42×C71 | C2 | semidirect |
| 8. C23×Dic142 | C22 | semidirect |
| 12. C2×#14556116 | C22 | direct (N × H) |
| 13. C22×(C2×D71)⋊C4 | C22 | semidirect |
| 16. C22×C42×C71 | C22 | semidirect |
| 21. C22×Dic142 | C23 | semidirect |
| 26. #14556116 | C23 | direct (N × H) |
| 27. C2×(C2×D71)⋊C4 | C23 | semidirect |
| 33. C2×C42×C71 | C23 | semidirect |
| 39. C2×Dic142 | C24 | semidirect |
| 44. (C2×D71)⋊C4 | C24 | semidirect |
| 52. C42×C71 | C24 | semidirect |
| 53. C23×C71 | #124 | semidirect |
| 69. C22×C71 | C2×#124 | semidirect |
| 80. C2×C71 | C22×#124 | semidirect |
| 88. C23×C42 | D71 | semidirect |
| 89. C71 | C23×#124 | semidirect |
| 100. C22×C42 | C2×D71 | semidirect |
| 117. C2×C42 | C22×D71 | semidirect |
| 136. C42 | C23×D71 | semidirect |
| 141. C23 | #14556116 | direct (N × H) |
| 156. C22 | C2×#14556116 | direct (N × H) |
| 164. C2 | C22×#14556116 | 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 |
| C24×D284 | 2 |
| C22×#14556116 | 2 |
| C23×(C2×D71)⋊C4 | 2 |
| C23×C42×C71 | 2 |
| C23×#124 | 71 |