Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
656 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 656 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 |
|---|---|---|
| 3. #26042230 | C2 | semidirect |
| 5. C4×C4⋊#10624382 | C2 | semidirect |
| 18. #19153775 | C4 | semidirect |
| 19. #19153774 | C4 | semidirect |
| 20. #19153773 | C4 | semidirect |
| 21. #19153772 | C4 | semidirect |
| 25. #117×C181 | C4 | semidirect |
| 45. C4⋊Dic181 | C2×C4 | semidirect |
| 46. #15668428 | C2×C4 | semidirect |
| 49. C4×Dic181 | C2×C4 | semidirect |
| 50. C4×Dic181 | C2×C4 | semidirect |
| 52. C4⋊C4×C181 | C2×C4 | semidirect |
| 54. C42×C181 | C2×C4 | semidirect |
| 66. C2×Dic181 | C4⋊C4 | semidirect |
| 71. C4×D181 | C4⋊C4 | semidirect |
| 72. C4×D181 | C4⋊C4 | semidirect |
| 78. C2×C4×C181 | C4⋊C4 | semidirect |
| 106. C181 | #2296 | semidirect |
| 121. #117 | #10624382 | semidirect |
| 151. C4⋊C4 | C2×#10624382 | semidirect |
| 161. C42 | C2×#10624382 | semidirect |
| 185. C2×C4 | C4⋊#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153895 | 2 |
| C22×C4×#10624382 | 2 |
| #26042230 | 2 |
| #26042226 | 2 |
| C4×C4⋊#10624382 | 2 |
| #117×D181 | 2 |
| #2296 | 181 |