Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 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×#19153847 | C2 | semidirect |
| 2. C2×#19153846 | C2 | semidirect |
| 4. C22×#15668439 | C2 | semidirect |
| 5. #26041855 | C2 | semidirect |
| 6. #26041674 | C2 | semidirect |
| 7. #26041671 | C2 | semidirect |
| 8. #26041661 | C2 | semidirect |
| 9. #26041658 | C2 | semidirect |
| 10. #26041235 | C2 | semidirect |
| 11. #536×C181 | C2 | semidirect |
| 143. C181 | #3156 | semidirect |
| 150. #536 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153847 | 2 |
| C2×#19153846 | 2 |
| C2×#19153836 | 2 |
| C22×#15668439 | 2 |
| #26041855 | 2 |
| #26041674 | 2 |
| #26041671 | 2 |
| #26041661 | 2 |
| #26041658 | 2 |
| #26041235 | 2 |
| #536×C181 | 2 |
| #3156 | 181 |