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 |
|---|---|---|
| 1. Q8×Dic23 | C2 | semidirect |
| 4. C23×#103 | C2 | semidirect |
| 6. C8×Dic23 | C2 | semidirect |
| 7. #10624990 | C2 | semidirect |
| 13. #67274 | C4 | semidirect |
| 22. Q8×C23 | C2×C4 | semidirect |
| 33. C23⋊C8 | C2×C4 | semidirect |
| 44. Dic23 | SD16 | semidirect |
| 54. #103 | D23 | semidirect |
| 57. C23 | C4×SD16 | semidirect |
| 72. Q8 | C4×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic23 | 2 |
| C2×#67274 | 2 |
| #10625064 | 2 |
| C23×#103 | 2 |
| #10625003 | 2 |
| C8×Dic23 | 2 |
| #10624990 | 2 |
| C4×SD16 | 23 |