Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
220 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 89 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×#19153756 | C2 | semidirect |
| 2. C2×#19153752 | C2 | semidirect |
| 3. #26041086 | C2 | semidirect |
| 8. C2×#15668424 | C22 | semidirect |
| 10. #19153752 | C22 | semidirect |
| 83. C181 | #2143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153756 | 2 |
| C2×#19153752 | 2 |
| #26041086 | 2 |
| C2×#135×C181 | 2 |
| #2143 | 181 |