Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
754 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19153845 | C2 | semidirect |
| 3. C22⋊Q8×D181 | C2 | semidirect |
| 4. #26041442 | C2 | semidirect |
| 5. #26041438 | C2 | semidirect |
| 6. #26041437 | C2 | semidirect |
| 7. #26041434 | C2 | semidirect |
| 8. #26041430 | C2 | semidirect |
| 9. #26041277 | C2 | semidirect |
| 10. #26041241 | C2 | semidirect |
| 11. #450×C181 | C2 | semidirect |
| 18. C2×Q8×D181 | C22 | semidirect |
| 23. C2×Dic724 | C22 | semidirect |
| 24. C2×#15668439 | C22 | semidirect |
| 25. C2×#15668437 | C22 | semidirect |
| 26. C2×#15668432 | C22 | semidirect |
| 27. #19153796 | C22 | semidirect |
| 31. #19153792 | C22 | semidirect |
| 33. C4⋊C4×D181 | C22 | semidirect |
| 35. #19153741 | C22 | semidirect |
| 36. #19153739 | C22 | semidirect |
| 37. #19153737 | C22 | semidirect |
| 39. #19153728 | C22 | semidirect |
| 41. C2×SD16×C181 | C22 | semidirect |
| 43. #102×C181 | C22 | semidirect |
| 146. C22×C181 | #137 | semidirect |
| 171. C181 | #3007 | semidirect |
| 181. #450 | D181 | semidirect |
| 199. C2×SD16 | C2×D181 | semidirect |
| 213. #102 | C2×D181 | semidirect |
| 325. C22 | #19153845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668448 | 2 |
| C2×#19153845 | 2 |
| C22⋊Q8×D181 | 2 |
| #26041442 | 2 |
| #26041438 | 2 |
| #26041437 | 2 |
| #26041434 | 2 |
| #26041430 | 2 |
| #26041277 | 2 |
| #26041241 | 2 |
| #450×C181 | 2 |
| #3007 | 181 |