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 |
|---|---|---|
| 2. C22×#14556117 | C2 | direct (N × H) |
| 3. C23×(C2×D71)⋊C4 | C2 | semidirect |
| 4. C23×C4×Dic71 | C2 | semidirect |
| 5. C24×Q8×C71 | C2 | semidirect |
| 10. C2×#14556117 | C22 | direct (N × H) |
| 11. C22×(C2×D71)⋊C4 | C22 | semidirect |
| 12. C22×C4×Dic71 | C22 | semidirect |
| 14. C23×Q8×C71 | C22 | semidirect |
| 24. #14556117 | C23 | direct (N × H) |
| 25. C2×(C2×D71)⋊C4 | C23 | semidirect |
| 26. C2×C4×Dic71 | C23 | semidirect |
| 29. C22×Q8×C71 | C23 | semidirect |
| 42. (C2×D71)⋊C4 | C24 | semidirect |
| 43. C4×Dic71 | C24 | semidirect |
| 48. C2×Q8×C71 | C24 | semidirect |
| 53. C23×C71 | #124 | semidirect |
| 69. C22×C71 | C2×#124 | semidirect |
| 80. C2×C71 | C22×#124 | semidirect |
| 84. C24×Q8 | D71 | semidirect |
| 89. C71 | C23×#124 | semidirect |
| 92. C23×Q8 | C2×D71 | semidirect |
| 106. C22×Q8 | C22×D71 | semidirect |
| 126. C2×Q8 | C23×D71 | semidirect |
| 141. C23 | #14556117 | direct (N × H) |
| 156. C22 | C2×#14556117 | direct (N × H) |
| 164. C2 | C22×#14556117 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D284 | 2 |
| C22×#14556117 | 2 |
| C23×(C2×D71)⋊C4 | 2 |
| C23×C4×Dic71 | 2 |
| C24×Q8×C71 | 2 |
| C23×#124 | 71 |