Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
820 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 1. C2×#19153876 | C2 | semidirect |
| 2. #26042249 | C2 | semidirect |
| 4. C2×#15668458 | C22 | semidirect |
| 73. C22×C181 | #100 | semidirect |
| 89. C181 | #1783 | semidirect |
| 168. C22 | #19153876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153876 | 2 |
| #26042249 | 2 |
| C23×C22⋊D181 | 2 |
| #1783 | 181 |