Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
168 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 2. #26041564 | C2 | semidirect |
| 3. #26041410 | C2 | semidirect |
| 4. #26041031 | C2 | semidirect |
| 5. #26041024 | C2 | semidirect |
| 48. #13089678 | SD16 | semidirect |
| 79. C181 | #1686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041651 | 2 |
| #26041564 | 2 |
| #26041410 | 2 |
| #26041031 | 2 |
| #26041024 | 2 |
| #26041023 | 2 |
| #460×C181 | 2 |
| #1686 | 181 |