Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1880 conjugacy classes of subgroups; only the 981 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 981 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. C2×#19153723 | C2 | direct (N × H) |
| 6. C23×Dic181 | C4 | semidirect |
| 8. #19153723 | C22 | direct (N × H) |
| 11. C23×C4×C181 | C4 | semidirect |
| 16. C22×Dic181 | C2×C4 | semidirect |
| 26. C22×C4×C181 | C2×C4 | semidirect |
| 31. C2×Dic181 | C22×C4 | semidirect |
| 45. C2×C4×C181 | C22×C4 | semidirect |
| 46. C22×C181 | #95 | semidirect |
| 59. C2×C181 | C2×#95 | semidirect |
| 65. C181 | C22×#95 | semidirect |
| 76. C23×C4 | Dic181 | semidirect |
| 92. C22×C4 | C2×Dic181 | semidirect |
| 111. C2×C4 | C22×Dic181 | semidirect |
| 112. C22 | #19153723 | direct (N × H) |
| 125. C2 | C2×#19153723 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic181 | 2 |
| C2×#19153723 | 2 |
| C24×C4×C181 | 2 |
| C22×#95 | 181 |