Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
688 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 152 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. #26042231 | C2 | semidirect |
| 2. #26042229 | C2 | semidirect |
| 3. #26042227 | C2 | semidirect |
| 4. #26042220 | C2 | semidirect |
| 6. C23×#10624382 | C22 | semidirect |
| 7. C2×C4⋊#10624382 | C22 | semidirect |
| 10. C2×C22⋊#10624382 | C22 | semidirect |
| 11. C2×C4×#10624382 | C22 | semidirect |
| 12. (C2×#10624382)⋊C4 | C22 | semidirect |
| 15. #19153786 | C4 | semidirect |
| 16. #19153785 | C4 | semidirect |
| 17. #19153784 | C4 | semidirect |
| 19. #120×C181 | C4 | semidirect |
| 30. C23×D181 | C2×C4 | semidirect |
| 39. C22⋊Dic181 | C2×C4 | semidirect |
| 40. #15668426 | C2×C4 | semidirect |
| 41. C24×C181 | C2×C4 | semidirect |
| 43. C22⋊C4×C181 | C2×C4 | semidirect |
| 100. C181 | #2375 | semidirect |
| 113. #120 | #10624382 | semidirect |
| 126. C24 | C2×#10624382 | semidirect |
| 143. C22⋊C4 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042231 | 2 |
| #26042229 | 2 |
| #26042227 | 2 |
| #26042220 | 2 |
| #120×D181 | 2 |
| #2375 | 181 |