Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
226 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 57 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. C22×Dic724 | C2 | semidirect |
| 2. C2×#19153760 | C2 | semidirect |
| 3. #26041082 | C2 | semidirect |
| 4. C22⋊#15668424 | C2 | semidirect |
| 24. Dic724 | D4 | semidirect |
| 57. C22×C181 | SD32 | semidirect |
| 69. C181 | #2185 | semidirect |
| 127. C22 | #19153760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic724 | 2 |
| C2×#19153760 | 2 |
| #26041082 | 2 |
| C22⋊#15668424 | 2 |
| #466×C181 | 2 |
| #2185 | 181 |