Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
402 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 157 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. #26041358 | C2 | semidirect |
| 3. #26041356 | C2 | semidirect |
| 4. #26041352 | C2 | semidirect |
| 5. #26041349 | C2 | semidirect |
| 6. #26041340 | C2 | semidirect |
| 7. #26041244 | C2 | semidirect |
| 8. #26041241 | C2 | semidirect |
| 9. #433×C181 | C2 | semidirect |
| 14. C2×#15668432 | C22 | semidirect |
| 15. C2×C8×D181 | C22 | semidirect |
| 22. C4⋊#13089678 | C22 | semidirect |
| 26. #19153728 | C22 | semidirect |
| 27. #19153728 | C22 | semidirect |
| 28. #19153727 | C22 | semidirect |
| 29. C4×#13089678 | C22 | semidirect |
| 31. C4⋊C8×C181 | C22 | semidirect |
| 33. #97×C181 | C22 | semidirect |
| 34. C4×C8×C181 | C22 | semidirect |
| 114. C181 | #2978 | semidirect |
| 122. #433 | D181 | semidirect |
| 139. C4⋊C8 | C2×D181 | semidirect |
| 147. #97 | C2×D181 | semidirect |
| 149. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041791 | 2 |
| #26041358 | 2 |
| #26041356 | 2 |
| #26041352 | 2 |
| #26041349 | 2 |
| #26041340 | 2 |
| #26041244 | 2 |
| #26041241 | 2 |
| #433×C181 | 2 |
| #2978 | 181 |