Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26041910 | C2 | semidirect |
| 3. #26041582 | C2 | semidirect |
| 4. #26041578 | C2 | semidirect |
| 5. #26041568 | C2 | semidirect |
| 6. #26041558 | C2 | semidirect |
| 7. #26041315 | C2 | semidirect |
| 8. #26041307 | C2 | semidirect |
| 11. #428×C181 | C2 | semidirect |
| 15. #19153815 | C22 | semidirect |
| 17. #19153807 | C22 | semidirect |
| 26. #19153749 | C22 | semidirect |
| 27. #19153749 | C22 | semidirect |
| 28. #19153747 | C22 | semidirect |
| 29. #19153747 | C22 | semidirect |
| 30. #19153745 | C22 | semidirect |
| 31. #19153745 | C22 | semidirect |
| 39. #107×C181 | C22 | semidirect |
| 40. #106×C181 | C22 | semidirect |
| 45. C2×D724 | Q8 | semidirect |
| 124. C181 | #3081 | semidirect |
| 132. #428 | D181 | semidirect |
| 156. #107 | C2×D181 | semidirect |
| 159. #106 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041910 | 2 |
| #26041753 | 2 |
| #26041582 | 2 |
| #26041578 | 2 |
| #26041568 | 2 |
| #26041558 | 2 |
| #26041315 | 2 |
| #26041307 | 2 |
| #26041285 | 2 |
| C2×#19153736 | 2 |
| #428×C181 | 2 |
| #3081 | 181 |