Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 218 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. C22×C22⋊#10624382 | C2 | semidirect |
| 2. C2×#19153874 | C2 | direct (N × H) |
| 6. C2×C22⋊#10624382 | C22 | semidirect |
| 7. #19153874 | C22 | direct (N × H) |
| 11. C22×C22⋊D181 | C4 | semidirect |
| 13. C23×Dic181 | C4 | semidirect |
| 14. C25×C181 | C4 | semidirect |
| 18. C22⋊#10624382 | C23 | semidirect |
| 28. C2×C22⋊D181 | C2×C4 | semidirect |
| 32. C22×Dic181 | C2×C4 | semidirect |
| 37. C24×C181 | C2×C4 | semidirect |
| 54. C2×Dic181 | C22×C4 | semidirect |
| 64. C23×C181 | C22×C4 | semidirect |
| 71. C22×C181 | #99 | semidirect |
| 88. C2×C181 | C2×#99 | semidirect |
| 92. C181 | C22×#99 | semidirect |
| 98. C25 | #10624382 | semidirect |
| 117. C24 | C2×#10624382 | semidirect |
| 150. C23 | C22×#10624382 | semidirect |
| 172. C22 | #19153874 | direct (N × H) |
| 183. C2 | C2×#19153874 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#10624382 | 2 |
| C2×#19153874 | 2 |
| C23×C22⋊D181 | 2 |
| C22×#99 | 181 |