Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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. #26042294 | C2 | semidirect |
| 4. M16×#10624382 | C2 | semidirect |
| 5. #26042162 | C2 | semidirect |
| 6. #26042151 | C2 | semidirect |
| 23. #19153735 | C4 | semidirect |
| 24. #19153732 | C4 | semidirect |
| 25. #19153732 | C4 | semidirect |
| 26. #101×C181 | C4 | semidirect |
| 105. C181 | #1932 | semidirect |
| 128. #101 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042294 | 2 |
| #26042278 | 2 |
| C2×#19153881 | 2 |
| M16×#10624382 | 2 |
| #26042162 | 2 |
| #26042151 | 2 |
| #26041262 | 2 |
| #1932 | 181 |