Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 122 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. C2×#19153871 | C2 | semidirect |
| 4. #26042145 | C2 | semidirect |
| 7. C22×#13089685 | C4 | semidirect |
| 11. C22⋊#13089685 | C4 | semidirect |
| 41. #13089685 | C22⋊C4 | semidirect |
| 67. C22×C181 | #97 | semidirect |
| 85. C181 | #1752 | semidirect |
| 153. C22 | #19153871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13089685 | 2 |
| C2×C22⋊#13089685 | 2 |
| C2×#19153871 | 2 |
| #26042145 | 2 |
| C22⋊C4×Dic181 | 2 |
| #1752 | 181 |