Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26042002 | C2 | semidirect |
| 3. #26041626 | C2 | semidirect |
| 4. #26041605 | C2 | semidirect |
| 5. #26041559 | C2 | semidirect |
| 6. #26041528 | C2 | semidirect |
| 7. #26041479 | C2 | semidirect |
| 8. #26041428 | C2 | semidirect |
| 9. #26041358 | C2 | semidirect |
| 10. #26041282 | C2 | semidirect |
| 11. C4×SD16×C181 | C2 | semidirect |
| 14. C2×#15668436 | C22 | semidirect |
| 15. C2×#15668432 | C22 | semidirect |
| 16. #19153816 | C22 | semidirect |
| 20. #19153792 | C22 | semidirect |
| 26. #19153774 | C22 | semidirect |
| 27. #19153749 | C22 | semidirect |
| 28. C4⋊#13089678 | C22 | semidirect |
| 29. #19153738 | C22 | semidirect |
| 30. #19153738 | C22 | semidirect |
| 32. #19153736 | C22 | semidirect |
| 33. #19153728 | C22 | semidirect |
| 35. C4×Q8×C181 | C22 | semidirect |
| 37. #106×C181 | C22 | semidirect |
| 38. #103×C181 | C22 | semidirect |
| 40. C4×C8×C181 | C22 | semidirect |
| 135. C181 | #3324 | semidirect |
| 145. C4×SD16 | D181 | semidirect |
| 162. C4×Q8 | C2×D181 | semidirect |
| 167. #106 | C2×D181 | semidirect |
| 169. #103 | C2×D181 | semidirect |
| 176. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042002 | 2 |
| D4×D724 | 2 |
| #26041626 | 2 |
| #26041605 | 2 |
| #26041559 | 2 |
| #26041528 | 2 |
| #26041479 | 2 |
| #26041428 | 2 |
| #26041358 | 2 |
| #26041282 | 2 |
| C4×SD16×C181 | 2 |
| #3324 | 181 |