Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 200 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 |
|---|---|---|
| 8. #19153870 | C4 | semidirect |
| 9. C8×#10624382 | C4 | semidirect |
| 13. #19153727 | C4 | semidirect |
| 14. #19153726 | C4 | semidirect |
| 15. C8×Dic181 | C4 | semidirect |
| 16. C4×C8×C181 | C4 | semidirect |
| 61. C181 | #1747 | semidirect |
| 78. C4×C8 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042242 | 2 |
| #26042148 | 2 |
| #26042147 | 2 |
| #26042146 | 2 |
| #26041233 | 2 |
| #1747 | 181 |