Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
104 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 39 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. C23×#131 | C2 | semidirect |
| 2. #10625122 | C2 | semidirect |
| 4. C2×#67263 | C2 | semidirect |
| 5. #10625006 | C2 | semidirect |
| 6. #10625005 | C2 | semidirect |
| 7. #10625001 | C2 | semidirect |
| 55. #131 | D23 | semidirect |
| 59. C23 | #471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#131 | 2 |
| #10625122 | 2 |
| #10625120 | 2 |
| C2×#67263 | 2 |
| #10625006 | 2 |
| #10625005 | 2 |
| #10625001 | 2 |
| #471 | 23 |