Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26042084 | C2 | semidirect |
| 2. #26041715 | C2 | semidirect |
| 3. #26041714 | C2 | semidirect |
| 4. #26041709 | C2 | semidirect |
| 5. C2×#19153757 | C2 | semidirect |
| 6. #26041696 | C2 | semidirect |
| 7. #576×C181 | C2 | semidirect |
| 10. #19153838 | C22 | semidirect |
| 11. C2×D1448 | C22 | semidirect |
| 12. #19153762 | C22 | semidirect |
| 13. #19153760 | C22 | semidirect |
| 14. #19153759 | C22 | semidirect |
| 15. #19153757 | C22 | semidirect |
| 16. #19153757 | C22 | semidirect |
| 17. #19153756 | C22 | semidirect |
| 18. C2×#15668424 | C22 | semidirect |
| 21. #135×C181 | C22 | semidirect |
| 22. C2×D8×C181 | C22 | semidirect |
| 75. C181 | #3415 | semidirect |
| 78. #576 | D181 | semidirect |
| 89. #135 | C2×D181 | semidirect |
| 91. C2×D8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042084 | 2 |
| #26041715 | 2 |
| #26041714 | 2 |
| #26041709 | 2 |
| C2×#19153757 | 2 |
| #26041696 | 2 |
| #576×C181 | 2 |
| #3415 | 181 |