Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
390 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 2. C2×#19153781 | C2 | semidirect |
| 4. #26041589 | C2 | semidirect |
| 5. #26041504 | C2 | semidirect |
| 6. #26041434 | C2 | semidirect |
| 8. #26041371 | C2 | semidirect |
| 9. #26041366 | C2 | semidirect |
| 10. #26041329 | C2 | semidirect |
| 11. #483×C181 | C2 | semidirect |
| 131. C181 | #3108 | semidirect |
| 135. #483 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041815 | 2 |
| C2×#19153781 | 2 |
| #26041592 | 2 |
| #26041589 | 2 |
| #26041504 | 2 |
| #26041434 | 2 |
| #26041420 | 2 |
| #26041371 | 2 |
| #26041366 | 2 |
| #26041329 | 2 |
| #483×C181 | 2 |
| #3108 | 181 |