Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
224 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 109 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×#19153756 | C2 | semidirect |
| 2. C22×#15668424 | C2 | semidirect |
| 3. #26041063 | C2 | direct (N × H) |
| 6. #19153756 | C22 | semidirect |
| 10. C2×#15668424 | C22 | semidirect |
| 80. C2×C181 | #350 | semidirect |
| 82. C181 | C2×#350 | semidirect |
| 163. C2 | #26041063 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153756 | 2 |
| C22×#15668424 | 2 |
| #26041063 | 2 |
| C2×#131×C181 | 2 |
| C2×#350 | 181 |