Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 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 |
|---|---|---|
| 2. C2×#19153847 | C2 | semidirect |
| 3. #26042045 | C2 | semidirect |
| 4. #26041551 | C2 | semidirect |
| 5. #26041539 | C2 | semidirect |
| 6. #26041328 | C2 | semidirect |
| 7. #26041263 | C2 | semidirect |
| 8. C2×#19153735 | C2 | semidirect |
| 9. C2×#137×C181 | C2 | semidirect |
| 26. #19153752 | C22 | semidirect |
| 27. #19153735 | C22 | semidirect |
| 28. #19153735 | C22 | semidirect |
| 29. #19153733 | C22 | semidirect |
| 34. C2×Q16×C181 | C22 | semidirect |
| 35. C2×SD16×C181 | C22 | semidirect |
| 142. C181 | #3069 | semidirect |
| 146. C2×#137 | D181 | semidirect |
| 166. C2×Q16 | C2×D181 | semidirect |
| 168. C2×SD16 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042077 | 2 |
| C2×#19153847 | 2 |
| #26042045 | 2 |
| #26041551 | 2 |
| #26041539 | 2 |
| #26041328 | 2 |
| #26041263 | 2 |
| C2×#19153735 | 2 |
| C2×#137×C181 | 2 |
| #3069 | 181 |