Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 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×M16×C23 | C2 | semidirect |
| 3. #10625095 | C2 | semidirect |
| 4. C2×#67263 | C2 | semidirect |
| 5. #10625003 | C2 | semidirect |
| 6. #10625000 | C2 | semidirect |
| 7. #10624998 | C2 | semidirect |
| 36. C8×C23 | D4 | semidirect |
| 57. C2×M16 | D23 | semidirect |
| 63. C23 | #468 | semidirect |
| 92. C8 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×C23 | 2 |
| #10625101 | 2 |
| #10625095 | 2 |
| C2×#67263 | 2 |
| #10625003 | 2 |
| #10625000 | 2 |
| #10624998 | 2 |
| #468 | 23 |