Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
352 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041675 | C2 | semidirect |
| 3. #26041617 | C2 | semidirect |
| 4. #26041603 | C2 | semidirect |
| 5. #26041574 | C2 | semidirect |
| 6. #26041556 | C2 | semidirect |
| 7. #26041510 | C2 | semidirect |
| 8. C4×#15668436 | C2 | semidirect |
| 9. D4×#13089678 | C2 | semidirect |
| 10. #26041315 | C2 | semidirect |
| 11. #556×C181 | C2 | semidirect |
| 120. C181 | #3340 | semidirect |
| 122. #556 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041994 | 2 |
| #26041675 | 2 |
| #26041617 | 2 |
| #26041603 | 2 |
| #26041574 | 2 |
| #26041556 | 2 |
| #26041510 | 2 |
| C4×#15668436 | 2 |
| D4×#13089678 | 2 |
| #26041315 | 2 |
| #556×C181 | 2 |
| #3340 | 181 |