Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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×C4×D724 | C2 | semidirect |
| 2. #26041590 | C2 | semidirect |
| 3. #26041556 | C2 | semidirect |
| 4. #26041471 | C2 | semidirect |
| 5. #26041412 | C2 | semidirect |
| 6. C4×#15668434 | C2 | semidirect |
| 7. #26041332 | C2 | semidirect |
| 8. #532×C181 | C2 | semidirect |
| 18. #19153749 | C22 | semidirect |
| 19. C4⋊#13089678 | C22 | semidirect |
| 20. #19153737 | C22 | semidirect |
| 23. C4×#13089678 | C22 | semidirect |
| 25. C4⋊Q8×C181 | C22 | semidirect |
| 26. #127×C181 | C22 | semidirect |
| 31. C4×D4×C181 | C22 | semidirect |
| 71. D724 | #41 | semidirect |
| 88. C2×C4×C181 | D8 | semidirect |
| 120. C181 | #3100 | semidirect |
| 122. #532 | D181 | semidirect |
| 134. C4⋊Q8 | C2×D181 | semidirect |
| 135. #127 | C2×D181 | semidirect |
| 144. C4×D4 | C2×D181 | semidirect |
| 208. C2×C4 | #15668434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D724 | 2 |
| #26041590 | 2 |
| #26041556 | 2 |
| #26041471 | 2 |
| #26041412 | 2 |
| C4×#15668434 | 2 |
| #26041332 | 2 |
| #532×C181 | 2 |
| #3100 | 181 |