Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×Dic724 | C2 | semidirect |
| 2. #26041719 | C2 | direct (N × H) |
| 3. C2×#19153762 | C2 | semidirect |
| 4. C2×#19153760 | C2 | semidirect |
| 5. C2×#19153756 | C2 | semidirect |
| 11. C2×Dic724 | C22 | semidirect |
| 12. #19153762 | C22 | semidirect |
| 13. #19153760 | C22 | semidirect |
| 14. #19153756 | C22 | semidirect |
| 81. C2×C181 | #510 | semidirect |
| 83. C181 | C2×#510 | semidirect |
| 165. C2 | #26041719 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic724 | 2 |
| #26041719 | 2 |
| C2×#19153762 | 2 |
| C2×#19153760 | 2 |
| C2×#19153756 | 2 |
| C2×#135×C181 | 2 |
| C2×#510 | 181 |