Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
256 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 66 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×#19153891 | C2 | semidirect |
| 2. C2×#19153886 | C2 | semidirect |
| 3. #26042197 | C2 | direct (N × H) |
| 7. #19153891 | C22 | semidirect |
| 10. #19153886 | C22 | semidirect |
| 83. C2×C181 | #361 | semidirect |
| 88. C181 | C2×#361 | semidirect |
| 175. C2 | #26042197 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153891 | 2 |
| C2×#19153886 | 2 |
| #26042197 | 2 |
| C2×D8×D181 | 2 |
| C2×#361 | 181 |