Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
412 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 90 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. C22⋊C4×#10624382 | C2 | semidirect |
| 4. #26042156 | C2 | semidirect |
| 6. C23×#10624382 | C4 | semidirect |
| 10. C2×C4⋊#10624382 | C4 | semidirect |
| 11. C2×C22⋊#10624382 | C4 | semidirect |
| 15. C2×C4×#10624382 | C4 | semidirect |
| 16. #19153875 | C4 | semidirect |
| 17. #19153874 | C4 | semidirect |
| 21. #19153731 | C4 | semidirect |
| 22. #19153730 | C4 | semidirect |
| 23. #99×C181 | C4 | semidirect |
| 39. C22⋊#10624382 | C2×C4 | semidirect |
| 52. C22⋊Dic181 | C2×C4 | semidirect |
| 55. C22⋊C4×C181 | C2×C4 | semidirect |
| 78. C22×D181 | C42 | semidirect |
| 87. C2×Dic181 | C42 | semidirect |
| 92. C23×C181 | C42 | semidirect |
| 96. C2×C4×C181 | C42 | semidirect |
| 121. #10624382 | #99 | direct (N × H) |
| 135. C181 | C4×#99 | semidirect |
| 158. #99 | #10624382 | direct (N × H) |
| 188. C22⋊C4 | C2×#10624382 | semidirect |
| 203. C23 | C4×#10624382 | semidirect |
| 232. 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×D4×#10624382 | 2 |
| D181⋊#99 | 2 |
| C22⋊C4×#10624382 | 2 |
| #26042156 | 2 |
| #99×D181 | 2 |
| C4×#99 | 181 |