Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
672 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 162 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. #26042229 | C2 | semidirect |
| 2. #26042221 | C2 | semidirect |
| 4. C4×C22⋊#10624382 | C2 | semidirect |
| 6. C2×C4⋊#10624382 | C22 | semidirect |
| 10. C2×C4×#10624382 | C22 | semidirect |
| 11. (C2×#10624382)⋊C4 | C22 | semidirect |
| 12. (C2×#10624382)⋊C4 | C22 | semidirect |
| 16. C2×C22⋊Dic181 | C4 | semidirect |
| 17. C2×#15668426 | C4 | semidirect |
| 18. C2×#15668426 | C4 | semidirect |
| 19. C22⋊C4×D181 | C4 | semidirect |
| 21. C2×C22⋊C4×C181 | C4 | semidirect |
| 120. C181 | #2312 | semidirect |
| 139. C2×C22⋊C4 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042229 | 2 |
| #26042221 | 2 |
| #26042220 | 2 |
| C4×C22⋊#10624382 | 2 |
| C2×C22⋊C4×D181 | 2 |
| #2312 | 181 |