Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
170 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 12. C4⋊Dic23 | C4 | semidirect |
| 39. C4×C23 | C4⋊C4 | semidirect |
| 56. C23 | #389 | semidirect |
| 93. C4 | Dic23⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×C23 | 2 |
| C2×C4⋊Dic23 | 2 |
| C2×Dic23⋊C4 | 2 |
| C2×C4×Dic23 | 2 |
| C23⋊#95 | 2 |
| #389 | 23 |