Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
128 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 43 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×SD16×C23 | C2 | semidirect |
| 2. Q8×Dic23 | C2 | semidirect |
| 3. C2×#67274 | C2 | semidirect |
| 5. #10625014 | C2 | semidirect |
| 6. #10625003 | C2 | semidirect |
| 7. Dic23⋊C8 | C2 | semidirect |
| 24. Q8×C23 | D4 | semidirect |
| 50. Dic23 | SD16 | semidirect |
| 58. C2×SD16 | D23 | semidirect |
| 64. C23 | #460 | semidirect |
| 81. Q8 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×C23 | 2 |
| Q8×Dic23 | 2 |
| C2×#67274 | 2 |
| #10625111 | 2 |
| #10625014 | 2 |
| #10625003 | 2 |
| Dic23⋊C8 | 2 |
| #460 | 23 |