Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
272 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 13. #19153871 | C4 | semidirect |
| 14. #19153871 | C4 | semidirect |
| 21. C4⋊#13089678 | C4 | semidirect |
| 22. #19153745 | C4 | semidirect |
| 23. #19153745 | C4 | semidirect |
| 24. C4⋊C8×C181 | C4 | semidirect |
| 60. #13089685 | C4⋊C4 | semidirect |
| 98. C181 | #1771 | semidirect |
| 118. C4⋊C8 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042238 | 2 |
| C2×#19153870 | 2 |
| C2×C8×#10624382 | 2 |
| C4×C4⋊#10624382 | 2 |
| (C2×#10624382)⋊C8 | 2 |
| C4⋊C8×D181 | 2 |
| #1771 | 181 |