Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
156 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26041106 | C2 | semidirect |
| 4. #26041104 | C2 | semidirect |
| 7. #19153756 | C4 | semidirect |
| 20. #15668424 | C2×C4 | semidirect |
| 55. C181 | #2159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153756 | 2 |
| #26041317 | 2 |
| #26041106 | 2 |
| #26041104 | 2 |
| C2×#107×C181 | 2 |
| #2159 | 181 |