Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
280 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 9. C4×#13089678 | C4 | semidirect |
| 10. C8×Dic181 | C4 | semidirect |
| 11. C4×C8×C181 | C4 | semidirect |
| 33. #13089678 | C4⋊C4 | semidirect |
| 36. C8×C181 | C4⋊C4 | semidirect |
| 43. C4×C181 | #107 | semidirect |
| 45. Dic181 | #107 | semidirect |
| 52. C181 | #1845 | semidirect |
| 64. C4×C8 | #10624382 | semidirect |
| 89. C8 | C4⋊#10624382 | semidirect |
| 98. C4 | #19153885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153885 | 2 |
| #26042225 | 2 |
| C4×C8×D181 | 2 |
| #1845 | 181 |