Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#19153837 | C2 | semidirect |
| 2. #26041951 | C2 | semidirect |
| 3. #26041949 | C2 | semidirect |
| 4. #26041655 | C2 | semidirect |
| 5. #26041514 | C2 | semidirect |
| 6. #26041480 | C2 | semidirect |
| 7. #26041425 | C2 | semidirect |
| 8. #26041423 | C2 | semidirect |
| 9. C4×#15668439 | C2 | semidirect |
| 10. #26041344 | C2 | semidirect |
| 11. #460×C181 | C2 | semidirect |
| 58. #15668439 | D4 | semidirect |
| 130. C4×C181 | #135 | semidirect |
| 142. C181 | #3287 | semidirect |
| 150. #460 | D181 | semidirect |
| 276. C4 | #19153837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153837 | 2 |
| #26041951 | 2 |
| #26041949 | 2 |
| #26041655 | 2 |
| #26041514 | 2 |
| #26041480 | 2 |
| #26041425 | 2 |
| #26041423 | 2 |
| C4×#15668439 | 2 |
| #26041344 | 2 |
| #460×C181 | 2 |
| #3287 | 181 |