Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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×#19153804 | C2 | semidirect |
| 2. #26041666 | C2 | semidirect |
| 3. #26041641 | C2 | semidirect |
| 4. #26041494 | C2 | semidirect |
| 5. #26041417 | C2 | semidirect |
| 6. #26041412 | C2 | semidirect |
| 7. #26041336 | C2 | semidirect |
| 8. #532×C181 | C2 | semidirect |
| 11. C2×#15668437 | C22 | semidirect |
| 19. C4⋊#13089678 | C22 | semidirect |
| 20. #19153739 | C22 | semidirect |
| 23. #19153727 | C22 | semidirect |
| 25. C4⋊Q8×C181 | C22 | semidirect |
| 26. #127×C181 | C22 | semidirect |
| 31. C4×D4×C181 | C22 | semidirect |
| 120. C181 | #3213 | semidirect |
| 122. #532 | D181 | semidirect |
| 135. C4⋊Q8 | C2×D181 | semidirect |
| 136. #127 | C2×D181 | semidirect |
| 145. C4×D4 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153804 | 2 |
| #26041666 | 2 |
| #26041641 | 2 |
| #26041494 | 2 |
| #26041417 | 2 |
| #26041412 | 2 |
| #26041336 | 2 |
| #532×C181 | 2 |
| #3213 | 181 |