Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. C2×#19153836 | C2 | semidirect |
| 2. #26041950 | C2 | semidirect |
| 3. #26041655 | C2 | semidirect |
| 4. #26041513 | C2 | semidirect |
| 5. #26041479 | C2 | semidirect |
| 6. #26041476 | C2 | semidirect |
| 7. #26041424 | C2 | semidirect |
| 8. #26041422 | C2 | semidirect |
| 9. C4×#15668439 | C2 | semidirect |
| 10. D4×#13089678 | C2 | semidirect |
| 11. #550×C181 | C2 | semidirect |
| 51. #15668439 | D4 | semidirect |
| 131. C4×C181 | #135 | semidirect |
| 142. C181 | #3287 | semidirect |
| 146. #550 | D181 | semidirect |
| 276. C4 | #19153836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153836 | 2 |
| #26041950 | 2 |
| #26041655 | 2 |
| #26041513 | 2 |
| #26041479 | 2 |
| #26041476 | 2 |
| #26041424 | 2 |
| #26041422 | 2 |
| C4×#15668439 | 2 |
| D4×#13089678 | 2 |
| #550×C181 | 2 |
| #3287 | 181 |