Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19153861 | C2 | semidirect |
| 2. C2×#19153842 | C2 | semidirect |
| 3. #26041446 | C2 | direct (N × H) |
| 4. C2×#19153744 | C2 | semidirect |
| 5. C2×#19153733 | C2 | semidirect |
| 6. C2×#127×C181 | C2 | semidirect |
| 9. #19153861 | C22 | semidirect |
| 15. #19153842 | C22 | semidirect |
| 18. C2×#15668433 | C22 | semidirect |
| 19. #19153744 | C22 | semidirect |
| 20. #19153733 | C22 | semidirect |
| 23. C22×D4×C181 | C22 | semidirect |
| 25. #127×C181 | C22 | semidirect |
| 26. C2×C42×C181 | C22 | semidirect |
| 30. #15668449 | D4 | semidirect |
| 34. C2×Dic362 | D4 | semidirect |
| 35. C2×D724 | D4 | semidirect |
| 47. #15668433 | C23 | semidirect |
| 60. C2×D4×C181 | C23 | semidirect |
| 64. C42×C181 | C23 | semidirect |
| 69. Dic362 | C2×D4 | semidirect |
| 71. D724 | C2×D4 | semidirect |
| 123. C2×C181 | #453 | semidirect |
| 126. C181 | C2×#453 | semidirect |
| 130. C2×#127 | D181 | semidirect |
| 143. C22×D4 | C2×D181 | semidirect |
| 150. #127 | C2×D181 | semidirect |
| 151. C2×C42 | C2×D181 | semidirect |
| 180. C2×D4 | C22×D181 | semidirect |
| 191. C42 | C22×D181 | semidirect |
| 251. C2 | #26041446 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153861 | 2 |
| C2×#19153842 | 2 |
| #26041446 | 2 |
| C2×#19153744 | 2 |
| C2×#19153733 | 2 |
| C2×#127×C181 | 2 |
| C2×#453 | 181 |