Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
568 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 10. C2×C4×#10624382 | C4 | semidirect |
| 13. (C2×#10624382)⋊C4 | C4 | semidirect |
| 16. #19153723 | C4 | semidirect |
| 17. #19153723 | C4 | semidirect |
| 18. #95×C181 | C4 | semidirect |
| 138. C181 | #1434 | semidirect |
| 157. #95 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#10624382 | 2 |
| C2×(C2×#10624382)⋊C4 | 2 |
| #95×D181 | 2 |
| #1434 | 181 |