Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. C4×D4×C23 | C2 | semidirect |
| 3. #10625107 | C2 | semidirect |
| 4. C4×C22⋊D23 | C2 | semidirect |
| 5. #10625097 | C2 | semidirect |
| 6. #10625068 | C2 | semidirect |
| 7. #10625061 | C2 | semidirect |
| 8. #10625054 | C2 | semidirect |
| 9. #10625050 | C2 | semidirect |
| 10. C42×D23 | C2 | semidirect |
| 11. C4×Dic46 | C2 | semidirect |
| 83. C4×D4 | D23 | semidirect |
| 86. C23 | #529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×C23 | 2 |
| #10625109 | 2 |
| #10625107 | 2 |
| C4×C22⋊D23 | 2 |
| #10625097 | 2 |
| #10625068 | 2 |
| #10625061 | 2 |
| #10625054 | 2 |
| #10625050 | 2 |
| C42×D23 | 2 |
| C4×Dic46 | 2 |
| #529 | 23 |