Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26041907 | C2 | semidirect |
| 5. #26041047 | C2 | semidirect |
| 6. #26041039 | C2 | semidirect |
| 7. #339×C181 | C2 | semidirect |
| 32. C2×D724 | Q8 | semidirect |
| 112. C181 | #2027 | semidirect |
| 120. #339 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041907 | 2 |
| #26041285 | 2 |
| #26041283 | 2 |
| #26041181 | 2 |
| #26041047 | 2 |
| #26041039 | 2 |
| #339×C181 | 2 |
| #2027 | 181 |