Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
344 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 78 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×#19153879 | C2 | semidirect |
| 3. #26042238 | C2 | semidirect |
| 4. #26042225 | C2 | semidirect |
| 14. #19153805 | C4 | semidirect |
| 15. #19153804 | C4 | semidirect |
| 16. #19153803 | C4 | semidirect |
| 20. #124×C181 | C4 | semidirect |
| 103. C181 | #1959 | semidirect |
| 117. #124 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153879 | 2 |
| C2×#19153878 | 2 |
| #26042238 | 2 |
| #26042225 | 2 |
| #124×D181 | 2 |
| #1959 | 181 |