Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19153849 | C2 | semidirect |
| 3. C22×#15668438 | C2 | semidirect |
| 4. C2×#19153822 | C2 | semidirect |
| 5. #26041543 | C2 | direct (N × H) |
| 6. C2×#19153734 | C2 | semidirect |
| 7. C2×#19153732 | C2 | semidirect |
| 8. C2×#108×C181 | C2 | semidirect |
| 13. #19153849 | C22 | semidirect |
| 22. C2×#15668438 | C22 | semidirect |
| 25. #19153822 | C22 | semidirect |
| 29. #19153734 | C22 | semidirect |
| 30. #19153732 | C22 | semidirect |
| 34. #108×C181 | C22 | semidirect |
| 134. C2×C181 | #471 | semidirect |
| 138. C181 | C2×#471 | semidirect |
| 145. C2×#108 | D181 | semidirect |
| 171. #108 | C2×D181 | semidirect |
| 275. C2 | #26041543 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| C2×#19153844 | 2 |
| C22×#15668438 | 2 |
| C2×#19153822 | 2 |
| #26041543 | 2 |
| C2×#19153734 | 2 |
| C2×#19153732 | 2 |
| C2×#108×C181 | 2 |
| C2×#471 | 181 |