Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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. #26041836 | C2 | semidirect |
| 2. #26041651 | C2 | semidirect |
| 3. #26041625 | C2 | semidirect |
| 4. #26041476 | C2 | semidirect |
| 5. #26041430 | C2 | semidirect |
| 6. #26041332 | C2 | semidirect |
| 8. C2×#15668437 | C22 | semidirect |
| 9. #19153816 | C22 | semidirect |
| 10. #19153816 | C22 | semidirect |
| 15. C4×Dic362 | C22 | semidirect |
| 17. C4⋊#13089678 | C22 | semidirect |
| 18. #19153737 | C22 | semidirect |
| 20. C4×#13089678 | C22 | semidirect |
| 76. C2×C4×C181 | SD16 | semidirect |
| 104. C181 | #3208 | semidirect |
| 180. C2×C4 | #15668437 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041836 | 2 |
| #26041651 | 2 |
| #26041625 | 2 |
| #26041476 | 2 |
| #26041430 | 2 |
| #26041332 | 2 |
| C2×#127×C181 | 2 |
| #3208 | 181 |