Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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. #26042359 | C2 | semidirect |
| 2. #26042325 | C2 | semidirect |
| 3. #26042323 | C2 | semidirect |
| 4. D181⋊#108 | C2 | semidirect |
| 5. #26042278 | C2 | semidirect |
| 6. #26042242 | C2 | semidirect |
| 9. #19153904 | C22 | semidirect |
| 14. #19153887 | C22 | semidirect |
| 15. #19153886 | C22 | semidirect |
| 16. #19153881 | C22 | semidirect |
| 17. #19153870 | C22 | semidirect |
| 18. C8×#10624382 | C22 | semidirect |
| 20. #19153839 | C4 | semidirect |
| 21. #19153839 | C4 | semidirect |
| 24. C2×#15668436 | C4 | semidirect |
| 25. C2×D1448 | C4 | semidirect |
| 27. C2×Q16×C181 | C4 | semidirect |
| 101. C181 | #2957 | semidirect |
| 115. C2×Q16 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042359 | 2 |
| #26042325 | 2 |
| #26042323 | 2 |
| D181⋊#108 | 2 |
| #26042278 | 2 |
| #26042242 | 2 |
| C2×#19153839 | 2 |
| #2957 | 181 |