Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
224 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 62 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. D181⋊M32 | C2 | semidirect |
| 2. #26042289 | C2 | semidirect |
| 3. #26042195 | C2 | semidirect |
| 6. #19153891 | C22 | semidirect |
| 10. #19153884 | C22 | semidirect |
| 14. #19153835 | C4 | semidirect |
| 16. C2×Dic724 | C4 | semidirect |
| 19. C2×D8×C181 | C4 | semidirect |
| 84. C181 | #2145 | semidirect |
| 97. C2×D8 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊M32 | 2 |
| #26042289 | 2 |
| #26042195 | 2 |
| C2×#19153835 | 2 |
| #2145 | 181 |