Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 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×#19153813 | C2 | semidirect |
| 2. #26041655 | C2 | semidirect |
| 3. #26041627 | C2 | semidirect |
| 4. #26041474 | C2 | semidirect |
| 5. #26041412 | C2 | semidirect |
| 6. #26041332 | C2 | semidirect |
| 7. #532×C181 | C2 | semidirect |
| 11. C2×#15668434 | C22 | semidirect |
| 16. C4⋊#13089678 | C22 | semidirect |
| 17. #19153736 | C22 | semidirect |
| 19. C4×#13089678 | C22 | semidirect |
| 21. C4⋊Q8×C181 | C22 | semidirect |
| 22. #127×C181 | C22 | semidirect |
| 27. C4×D4×C181 | C22 | semidirect |
| 81. C2×C4×C181 | D8 | semidirect |
| 112. C181 | #3205 | semidirect |
| 114. #532 | D181 | semidirect |
| 126. C4⋊Q8 | C2×D181 | semidirect |
| 131. #127 | C2×D181 | semidirect |
| 136. C4×D4 | C2×D181 | semidirect |
| 193. C2×C4 | #15668434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153813 | 2 |
| #26041655 | 2 |
| #26041627 | 2 |
| #26041474 | 2 |
| #26041412 | 2 |
| #26041332 | 2 |
| #532×C181 | 2 |
| #3205 | 181 |