Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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×#19153824 | C2 | semidirect |
| 2. C22×#15668432 | C2 | semidirect |
| 4. #26041356 | C2 | semidirect |
| 5. #26041349 | C2 | semidirect |
| 6. #26041245 | C2 | semidirect |
| 7. #26041242 | C2 | semidirect |
| 8. #26041235 | C2 | semidirect |
| 9. #424×C181 | C2 | semidirect |
| 17. C2×#15668432 | C22 | semidirect |
| 19. C2×C8×D181 | C22 | semidirect |
| 26. #19153728 | C22 | semidirect |
| 27. #19153727 | C22 | semidirect |
| 28. C4×#13089678 | C22 | semidirect |
| 32. C4⋊C8×C181 | C22 | semidirect |
| 50. C2×#13089678 | D4 | semidirect |
| 113. C181 | #2930 | semidirect |
| 120. #424 | D181 | semidirect |
| 142. C4⋊C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153824 | 2 |
| C22×#15668432 | 2 |
| #26041791 | 2 |
| #26041356 | 2 |
| #26041349 | 2 |
| #26041245 | 2 |
| #26041242 | 2 |
| #26041235 | 2 |
| #424×C181 | 2 |
| #2930 | 181 |