Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
856 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 269 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×#15668433 | C2 | semidirect |
| 3. C2×#19153744 | C2 | direct (N × H) |
| 4. C22×C42×C181 | C2 | semidirect |
| 7. C2×#15668449 | C4 | semidirect |
| 9. C22×Dic362 | C4 | semidirect |
| 10. C22×D724 | C4 | semidirect |
| 14. C2×#15668433 | C22 | semidirect |
| 16. #19153744 | C22 | direct (N × H) |
| 20. C2×C42×C181 | C22 | semidirect |
| 25. #15668449 | C2×C4 | semidirect |
| 28. C2×Dic362 | C2×C4 | semidirect |
| 30. C2×D724 | C2×C4 | semidirect |
| 37. #15668433 | C23 | semidirect |
| 49. C42×C181 | C23 | semidirect |
| 53. Dic362 | C22×C4 | semidirect |
| 55. D724 | C22×C4 | semidirect |
| 79. C22×C181 | #104 | semidirect |
| 93. C2×C181 | C2×#104 | semidirect |
| 96. C181 | C22×#104 | semidirect |
| 100. C22×C42 | D181 | semidirect |
| 116. C2×C42 | C2×D181 | semidirect |
| 146. C42 | C22×D181 | semidirect |
| 178. C22 | #19153744 | direct (N × H) |
| 191. C2 | C2×#19153744 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668449 | 2 |
| C22×#15668433 | 2 |
| C2×#19153744 | 2 |
| C22×C42×C181 | 2 |
| C22×#104 | 181 |