Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. C22×#15668436 | C2 | semidirect |
| 3. #26041753 | C2 | semidirect |
| 4. #26041491 | C2 | semidirect |
| 5. #26041481 | C2 | semidirect |
| 6. #26041306 | C2 | semidirect |
| 7. #26041288 | C2 | semidirect |
| 8. #26041275 | C2 | semidirect |
| 9. #536×C181 | C2 | semidirect |
| 22. C4⋊#13089678 | C22 | semidirect |
| 23. #19153740 | C22 | semidirect |
| 24. #19153740 | C22 | semidirect |
| 25. #19153737 | C22 | semidirect |
| 28. C4⋊Q8×C181 | C22 | semidirect |
| 29. #124×C181 | C22 | semidirect |
| 116. C181 | #3042 | semidirect |
| 120. #536 | D181 | semidirect |
| 137. C4⋊Q8 | C2×D181 | semidirect |
| 138. #124 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153841 | 2 |
| C22×#15668436 | 2 |
| #26041753 | 2 |
| #26041491 | 2 |
| #26041481 | 2 |
| #26041306 | 2 |
| #26041288 | 2 |
| #26041275 | 2 |
| #536×C181 | 2 |
| #3042 | 181 |