Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #10625120 | C2 | semidirect |
| 3. #10625119 | C2 | semidirect |
| 4. C2×#67272 | C2 | semidirect |
| 5. #10625015 | C2 | semidirect |
| 6. #10625005 | C2 | semidirect |
| 7. #10625004 | C2 | semidirect |
| 55. AGL(1,ℤ/8) | D23 | semidirect |
| 61. C23 | #472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×AGL(1,ℤ/8) | 2 |
| #10625120 | 2 |
| #10625119 | 2 |
| C2×#67272 | 2 |
| #10625015 | 2 |
| #10625005 | 2 |
| #10625004 | 2 |
| #472 | 23 |