Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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×#19153822 | C2 | semidirect |
| 2. #26041853 | C2 | semidirect |
| 4. #26041522 | C2 | semidirect |
| 5. #26041505 | C2 | semidirect |
| 6. #26041317 | C2 | semidirect |
| 7. #26041288 | C2 | semidirect |
| 8. #26041284 | C2 | semidirect |
| 9. C22×SD16×C181 | C2 | semidirect |
| 13. C2×#15668432 | C22 | semidirect |
| 14. C2×C8×D181 | C22 | semidirect |
| 20. #19153792 | C22 | semidirect |
| 25. #19153750 | C22 | semidirect |
| 26. #19153748 | C22 | semidirect |
| 27. #19153740 | C22 | semidirect |
| 68. C2×C8×C181 | D4 | semidirect |
| 120. C181 | #3057 | semidirect |
| 122. C22×SD16 | D181 | semidirect |
| 180. C2×C8 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153822 | 2 |
| #26041853 | 2 |
| #26041846 | 2 |
| #26041522 | 2 |
| #26041505 | 2 |
| #26041317 | 2 |
| #26041288 | 2 |
| #26041284 | 2 |
| C22×SD16×C181 | 2 |
| #3057 | 181 |