Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19153845 | C2 | semidirect |
| 2. C2×#19153840 | C2 | semidirect |
| 3. #26041827 | C2 | semidirect |
| 4. #124×D181 | C2 | semidirect |
| 5. #26041674 | C2 | semidirect |
| 6. #26041673 | C2 | semidirect |
| 7. #26041666 | C2 | semidirect |
| 8. #26041662 | C2 | semidirect |
| 9. #26041660 | C2 | semidirect |
| 10. #26041231 | C2 | semidirect |
| 11. #496×C181 | C2 | semidirect |
| 17. C2×Dic724 | C22 | semidirect |
| 18. C2×#15668439 | C22 | semidirect |
| 21. C2×#15668437 | C22 | semidirect |
| 24. #19153816 | C22 | semidirect |
| 28. #19153803 | C22 | semidirect |
| 34. #19153727 | C22 | semidirect |
| 35. C8×Dic181 | C22 | semidirect |
| 36. C2×SD16×C181 | C22 | semidirect |
| 38. #127×C181 | C22 | semidirect |
| 40. #97×C181 | C22 | semidirect |
| 62. #15668432 | D4 | semidirect |
| 134. C181 | #3153 | semidirect |
| 143. #496 | D181 | semidirect |
| 157. C2×SD16 | C2×D181 | semidirect |
| 162. #127 | C2×D181 | semidirect |
| 174. #97 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153845 | 2 |
| C2×#19153840 | 2 |
| #26041827 | 2 |
| #124×D181 | 2 |
| #26041674 | 2 |
| #26041673 | 2 |
| #26041666 | 2 |
| #26041662 | 2 |
| #26041660 | 2 |
| #26041231 | 2 |
| #496×C181 | 2 |
| #3153 | 181 |