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. C22×C8×C23 | C2 | semidirect |
| 3. C2×#67267 | C2 | semidirect |
| 4. #10625072 | C2 | direct (N × H) |
| 5. C2×#67262 | C2 | semidirect |
| 6. C2×C8×D23 | C2 | semidirect |
| 16. C2×C8×C23 | C22 | semidirect |
| 17. #67267 | C22 | semidirect |
| 19. #67262 | C22 | semidirect |
| 20. C8×D23 | C22 | semidirect |
| 47. C2×C23 | #131 | semidirect |
| 55. C22×C8 | D23 | semidirect |
| 56. C23 | C2×#131 | semidirect |
| 70. C2×C8 | C2×D23 | semidirect |
| 97. C2 | #10625072 | 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 |
| C22×C8×C23 | 2 |
| C2×#67267 | 2 |
| #10625072 | 2 |
| C2×#67262 | 2 |
| C2×C8×D23 | 2 |
| C2×#131 | 23 |