Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
584 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 86 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×#19153877 | C2 | semidirect |
| 2. C2×#19153876 | C2 | semidirect |
| 3. #26042251 | C2 | semidirect |
| 111. C181 | #1785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153877 | 2 |
| C2×#19153876 | 2 |
| #26042251 | 2 |
| C22×#15668449 | 2 |
| #1785 | 181 |