Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
448 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 14. #19153808 | C4 | semidirect |
| 15. #19153807 | C4 | semidirect |
| 16. #19153806 | C4 | semidirect |
| 20. #125×C181 | C4 | semidirect |
| 70. C181 | #2371 | semidirect |
| 80. #125 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042228 | 2 |
| C4⋊C4×#10624382 | 2 |
| #26042215 | 2 |
| #125×D181 | 2 |
| #2371 | 181 |