Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#19153842 | C2 | semidirect |
| 2. #26041829 | C2 | semidirect |
| 3. #26041494 | C2 | semidirect |
| 4. #26041484 | C2 | semidirect |
| 5. #26041474 | C2 | semidirect |
| 6. #26041303 | C2 | semidirect |
| 7. #26041278 | C2 | semidirect |
| 8. C2×C4×D4×C181 | C2 | semidirect |
| 14. #19153816 | C22 | semidirect |
| 15. #19153813 | C22 | semidirect |
| 16. #19153804 | C22 | semidirect |
| 21. C4⋊#13089678 | C22 | semidirect |
| 22. C4⋊#13089678 | C22 | semidirect |
| 23. #19153739 | C22 | semidirect |
| 24. #19153736 | C22 | semidirect |
| 53. C2×D4×C181 | D4 | semidirect |
| 119. C4×C181 | AGL(1,ℤ/8) | semidirect |
| 129. C181 | #3036 | semidirect |
| 133. C2×C4×D4 | D181 | semidirect |
| 174. C2×D4 | D724 | semidirect |
| 250. C4 | #19153842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153842 | 2 |
| #26041829 | 2 |
| #26041494 | 2 |
| #26041484 | 2 |
| #26041474 | 2 |
| #26041303 | 2 |
| #26041278 | 2 |
| C2×C4×D4×C181 | 2 |
| #3036 | 181 |