Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 1. C2×#19153846 | C2 | semidirect |
| 2. C22×#15668437 | C2 | semidirect |
| 3. #26041756 | C2 | semidirect |
| 4. #26041498 | C2 | semidirect |
| 5. #26041476 | C2 | semidirect |
| 6. #26041306 | C2 | semidirect |
| 7. #26041284 | C2 | semidirect |
| 8. #26041275 | C2 | semidirect |
| 12. C2×#15668439 | C22 | semidirect |
| 15. C2×#15668437 | C22 | semidirect |
| 18. C4×Dic362 | C22 | semidirect |
| 22. C4⋊#13089678 | C22 | semidirect |
| 23. #19153740 | C22 | semidirect |
| 25. #19153737 | C22 | semidirect |
| 35. C2×Dic362 | D4 | semidirect |
| 116. C181 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153846 | 2 |
| C22×#15668437 | 2 |
| #26041756 | 2 |
| #26041498 | 2 |
| #26041476 | 2 |
| #26041306 | 2 |
| #26041284 | 2 |
| #26041275 | 2 |
| #535×C181 | 2 |
| #3043 | 181 |