Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
912 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 290 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 |
|---|---|---|
| 2. C22⋊C4×#10624382 | C2 | semidirect |
| 3. C4×C22⋊#10624382 | C2 | semidirect |
| 6. C2×C22⋊#10624382 | C4 | semidirect |
| 9. C2×C4×#10624382 | C22 | semidirect |
| 10. (C2×#10624382)⋊C4 | C22 | semidirect |
| 13. C2×C22⋊Dic181 | C4 | semidirect |
| 14. C2×#15668426 | C4 | semidirect |
| 15. C22⋊C4×D181 | C4 | semidirect |
| 17. C2×C22⋊C4×C181 | C4 | semidirect |
| 19. C22×#10624382 | C2×C4 | semidirect |
| 21. C22⋊#10624382 | C2×C4 | semidirect |
| 22. C22⋊#10624382 | C2×C4 | semidirect |
| 30. C22×Dic181 | C2×C4 | semidirect |
| 32. C2×C4×D181 | C2×C4 | semidirect |
| 34. C22⋊Dic181 | C2×C4 | semidirect |
| 35. #15668426 | C2×C4 | semidirect |
| 37. C22×C4×C181 | C2×C4 | semidirect |
| 38. C22⋊C4×C181 | C2×C4 | semidirect |
| 47. C22×D181 | C42 | semidirect |
| 48. C22×D181 | C42 | semidirect |
| 60. C23×C181 | C42 | semidirect |
| 92. C181 | #2273 | semidirect |
| 108. C2×C22⋊C4 | #10624382 | semidirect |
| 125. C22×C4 | C2×#10624382 | semidirect |
| 130. C22⋊C4 | C2×#10624382 | semidirect |
| 146. C23 | C4×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#10624382 | 2 |
| C22⋊C4×#10624382 | 2 |
| C4×C22⋊#10624382 | 2 |
| C2×C22⋊C4×D181 | 2 |
| #2273 | 181 |