Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. #26041627 | C2 | semidirect |
| 3. #26041597 | C2 | semidirect |
| 4. #26041566 | C2 | semidirect |
| 5. #26041510 | C2 | semidirect |
| 6. #26041479 | C2 | semidirect |
| 7. #26041429 | C2 | semidirect |
| 8. C4×#15668436 | C2 | semidirect |
| 9. D4×#13089678 | C2 | semidirect |
| 10. C2×#19153736 | C2 | semidirect |
| 11. #554×C181 | C2 | semidirect |
| 15. C2×#15668436 | C22 | semidirect |
| 16. C22×#13089678 | C22 | semidirect |
| 22. #19153747 | C22 | semidirect |
| 23. #19153747 | C22 | semidirect |
| 24. C4⋊#13089678 | C22 | semidirect |
| 25. #19153740 | C22 | semidirect |
| 28. #19153736 | C22 | semidirect |
| 29. #19153736 | C22 | semidirect |
| 30. #19153736 | C22 | semidirect |
| 31. C22⋊#13089678 | C22 | semidirect |
| 32. C4×#13089678 | C22 | semidirect |
| 33. C4⋊Q8×C181 | C22 | semidirect |
| 36. C22⋊Q8×C181 | C22 | semidirect |
| 37. C4×Q8×C181 | C22 | semidirect |
| 40. C2×C4⋊C4×C181 | C22 | semidirect |
| 99. D4×C181 | SD16 | semidirect |
| 136. C181 | #3295 | semidirect |
| 138. #554 | D181 | semidirect |
| 154. C4⋊Q8 | C2×D181 | semidirect |
| 158. C22⋊Q8 | C2×D181 | semidirect |
| 162. C4×Q8 | C2×D181 | semidirect |
| 166. C2×C4⋊C4 | C2×D181 | semidirect |
| 231. D4 | #15668436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D724 | 2 |
| #26041627 | 2 |
| #26041597 | 2 |
| #26041566 | 2 |
| #26041510 | 2 |
| #26041479 | 2 |
| #26041429 | 2 |
| C4×#15668436 | 2 |
| D4×#13089678 | 2 |
| C2×#19153736 | 2 |
| #554×C181 | 2 |
| #3295 | 181 |