Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
130 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 130 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. C23×#124 | C2 | semidirect |
| 2. C2×#67275 | C2 | semidirect |
| 3. C2×#67274 | C2 | semidirect |
| 4. C2×#67273 | C2 | semidirect |
| 6. #10625046 | C2 | semidirect |
| 7. C4×C23⋊C8 | C2 | semidirect |
| 57. #124 | D23 | semidirect |
| 59. C23 | #495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#124 | 2 |
| C2×#67275 | 2 |
| C2×#67274 | 2 |
| C2×#67273 | 2 |
| C2×#67272 | 2 |
| #10625046 | 2 |
| C4×C23⋊C8 | 2 |
| #495 | 23 |