Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 212 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 |
|---|---|---|
| 3. #26041486 | C2 | semidirect |
| 5. Q8⋊#13089678 | C2 | semidirect |
| 6. #26041009 | C2 | semidirect |
| 7. #475×C181 | C2 | semidirect |
| 90. C181 | #1640 | semidirect |
| 94. #475 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042014 | 2 |
| #26041627 | 2 |
| #26041486 | 2 |
| #26041022 | 2 |
| Q8⋊#13089678 | 2 |
| #26041009 | 2 |
| #475×C181 | 2 |
| #1640 | 181 |