Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 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×#19153838 | C2 | semidirect |
| 2. #26041790 | C2 | semidirect |
| 3. #26041537 | C2 | semidirect |
| 4. #26041532 | C2 | semidirect |
| 5. #26041525 | C2 | semidirect |
| 6. #26041317 | C2 | semidirect |
| 7. #26041276 | C2 | semidirect |
| 8. C22×M16×C181 | C2 | semidirect |
| 11. C2×Dic724 | C22 | semidirect |
| 12. C2×#15668438 | C22 | semidirect |
| 13. C2×D1448 | C22 | semidirect |
| 20. #19153750 | C22 | semidirect |
| 21. #19153748 | C22 | semidirect |
| 22. #19153741 | C22 | semidirect |
| 23. #19153738 | C22 | semidirect |
| 56. C2×C8×C181 | D4 | semidirect |
| 105. C181 | #3054 | semidirect |
| 108. C22×M16 | D181 | semidirect |
| 156. 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×#19153838 | 2 |
| #26041790 | 2 |
| #26041537 | 2 |
| #26041532 | 2 |
| #26041525 | 2 |
| #26041317 | 2 |
| #26041276 | 2 |
| C22×M16×C181 | 2 |
| #3054 | 181 |