Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#19153840 | C2 | semidirect |
| 2. #26041827 | C2 | semidirect |
| 3. #127×D181 | C2 | semidirect |
| 4. #26041667 | C2 | semidirect |
| 5. #26041655 | C2 | semidirect |
| 6. #26041652 | C2 | semidirect |
| 7. #26041651 | C2 | semidirect |
| 8. C4×#15668432 | C2 | semidirect |
| 9. #493×C181 | C2 | semidirect |
| 14. C2×#15668438 | C22 | semidirect |
| 15. C2×#15668437 | C22 | semidirect |
| 16. C2×#15668434 | C22 | semidirect |
| 18. #19153816 | C22 | semidirect |
| 22. #19153803 | C22 | semidirect |
| 26. #19153726 | C22 | semidirect |
| 27. C4×#13089678 | C22 | semidirect |
| 28. C2×D8×C181 | C22 | semidirect |
| 30. #127×C181 | C22 | semidirect |
| 31. C4×C8×C181 | C22 | semidirect |
| 48. #15668432 | D4 | semidirect |
| 77. #13089678 | C2×D4 | semidirect |
| 86. C8×C181 | C2×D4 | semidirect |
| 97. C4×C181 | AGL(1,ℤ/8) | semidirect |
| 108. C181 | #3151 | semidirect |
| 115. #493 | D181 | semidirect |
| 126. C2×D8 | C2×D181 | semidirect |
| 133. #127 | C2×D181 | semidirect |
| 140. C4×C8 | C2×D181 | semidirect |
| 195. C8 | D4×D181 | semidirect |
| 209. C4 | #19153840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153840 | 2 |
| #26041827 | 2 |
| #127×D181 | 2 |
| #26041667 | 2 |
| #26041655 | 2 |
| #26041652 | 2 |
| #26041651 | 2 |
| C4×#15668432 | 2 |
| #493×C181 | 2 |
| #3151 | 181 |