Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
266 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 2. C2×M16×C23 | C2 | semidirect |
| 3. C22×C23⋊C8 | C2 | semidirect |
| 4. #10625078 | C2 | direct (N × H) |
| 5. C2×#67262 | C2 | semidirect |
| 6. C2×C8×D23 | C2 | semidirect |
| 14. M16×C23 | C22 | semidirect |
| 18. C2×C23⋊C8 | C22 | semidirect |
| 19. #67262 | C22 | semidirect |
| 20. C8×D23 | C22 | semidirect |
| 47. C2×C23 | #131 | semidirect |
| 53. C2×M16 | D23 | semidirect |
| 56. C23 | C2×#131 | semidirect |
| 65. M16 | C2×D23 | semidirect |
| 97. C2 | #10625078 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67288 | 2 |
| C2×M16×C23 | 2 |
| C22×C23⋊C8 | 2 |
| #10625078 | 2 |
| C2×#67262 | 2 |
| C2×C8×D23 | 2 |
| C2×#131 | 23 |