Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
232 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 58 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. #26042290 | C2 | semidirect |
| 4. #26042245 | C2 | semidirect |
| 5. #26042158 | C2 | semidirect |
| 6. #26042154 | C2 | semidirect |
| 23. #19153733 | C4 | semidirect |
| 24. #19153732 | C4 | semidirect |
| 25. #19153732 | C4 | semidirect |
| 26. #100×C181 | C4 | semidirect |
| 114. C181 | #1931 | semidirect |
| 139. #100 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042290 | 2 |
| #26042271 | 2 |
| C2×#19153878 | 2 |
| #26042245 | 2 |
| #26042158 | 2 |
| #26042154 | 2 |
| #100×D181 | 2 |
| #1931 | 181 |