Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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 |
|---|---|---|
| 1. C2×#19153863 | C2 | semidirect |
| 2. C22×#15668437 | C2 | semidirect |
| 3. #26041846 | C2 | semidirect |
| 4. #26041421 | C2 | semidirect |
| 5. #26041416 | C2 | semidirect |
| 6. #26041289 | C2 | semidirect |
| 7. #26041275 | C2 | semidirect |
| 8. #26041247 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C181 | C2 | semidirect |
| 15. C2×#15668448 | C22 | semidirect |
| 18. C2×Q8×D181 | C22 | semidirect |
| 27. #19153741 | C22 | semidirect |
| 28. #19153740 | C22 | semidirect |
| 29. #19153737 | C22 | semidirect |
| 30. #19153728 | C22 | semidirect |
| 48. C2×Dic362 | D4 | semidirect |
| 69. #41×C181 | D4 | semidirect |
| 145. C181 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D181 | semidirect |
| 191. #41 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153863 | 2 |
| C22×#15668437 | 2 |
| #26041846 | 2 |
| #26041421 | 2 |
| #26041416 | 2 |
| #26041289 | 2 |
| #26041275 | 2 |
| #26041247 | 2 |
| C2×AGL(1,ℤ/8)×C181 | 2 |
| #3010 | 181 |