Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19153849 | C2 | semidirect |
| 3. C22×#15668437 | C2 | semidirect |
| 4. #26041855 | C2 | semidirect |
| 5. #26041442 | C2 | semidirect |
| 6. #26041431 | C2 | semidirect |
| 7. #26041273 | C2 | semidirect |
| 8. #26041247 | C2 | semidirect |
| 9. #418×C181 | C2 | semidirect |
| 16. C22×Dic362 | C22 | semidirect |
| 21. C2×Dic724 | C22 | semidirect |
| 22. C2×#15668438 | C22 | semidirect |
| 24. C2×#15668437 | C22 | semidirect |
| 25. C22×#13089678 | C22 | semidirect |
| 29. #19153796 | C22 | semidirect |
| 30. #19153739 | C22 | semidirect |
| 31. #19153736 | C22 | semidirect |
| 32. #19153728 | C22 | semidirect |
| 34. C2×M16×C181 | C22 | semidirect |
| 35. #117×C181 | C22 | semidirect |
| 36. #102×C181 | C22 | semidirect |
| 146. C181 | #3009 | semidirect |
| 154. #418 | D181 | semidirect |
| 173. C2×M16 | C2×D181 | semidirect |
| 179. #117 | C2×D181 | semidirect |
| 182. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153861 | 2 |
| C2×#19153849 | 2 |
| C22×#15668437 | 2 |
| #26041855 | 2 |
| #26041442 | 2 |
| #26041431 | 2 |
| #26041273 | 2 |
| #26041247 | 2 |
| #418×C181 | 2 |
| #3009 | 181 |