Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 3. #10625058 | C2 | semidirect |
| 5. #10624998 | C2 | semidirect |
| 6. C8×Dic23 | C2 | semidirect |
| 7. #10624990 | C2 | semidirect |
| 14. #67273 | C4 | semidirect |
| 31. Dic46 | C2×C4 | semidirect |
| 33. C23⋊C8 | C2×C4 | semidirect |
| 44. Dic23 | SD16 | semidirect |
| 57. C23 | C4×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic23 | 2 |
| C2×#67273 | 2 |
| #10625058 | 2 |
| C23×#102 | 2 |
| #10624998 | 2 |
| C8×Dic23 | 2 |
| #10624990 | 2 |
| C4×SD16 | 23 |