Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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×#67273 | C2 | semidirect |
| 3. #10625095 | C2 | semidirect |
| 4. C22×C23⋊C8 | C2 | semidirect |
| 5. #10625014 | C2 | semidirect |
| 6. #10624992 | C2 | semidirect |
| 7. #10624990 | C2 | semidirect |
| 36. C23⋊C8 | D4 | semidirect |
| 42. C22×C23 | SD16 | semidirect |
| 63. C23 | #465 | semidirect |
| 98. C22 | #67273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#121 | 2 |
| C2×#67273 | 2 |
| #10625095 | 2 |
| C22×C23⋊C8 | 2 |
| #10625014 | 2 |
| #10624992 | 2 |
| #10624990 | 2 |
| #465 | 23 |