Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
168 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #26041031 | C2 | semidirect |
| 4. #26041029 | C2 | semidirect |
| 66. C181 | #1568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041336 | 2 |
| C2×C4×#13089678 | 2 |
| #26041031 | 2 |
| #26041029 | 2 |
| #432×C181 | 2 |
| #1568 | 181 |