Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19153727 | C2 | semidirect |
| 4. #26041034 | C2 | semidirect |
| 7. C22×#13089678 | C4 | semidirect |
| 11. C22⋊#13089678 | C4 | semidirect |
| 38. #13089678 | C22⋊C4 | semidirect |
| 59. C22×C181 | #97 | semidirect |
| 74. C181 | #1752 | semidirect |
| 134. C22 | #19153727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13089678 | 2 |
| C2×C22⋊#13089678 | 2 |
| C2×#19153727 | 2 |
| #26041034 | 2 |
| C4×C22⋊C4×C181 | 2 |
| #1752 | 181 |