Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 140 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. C2×D8×C23 | C2 | semidirect |
| 2. #10625111 | C2 | semidirect |
| 3. D4×Dic23 | C2 | semidirect |
| 4. C2×#67272 | C2 | semidirect |
| 5. #10625014 | C2 | semidirect |
| 6. #10625003 | C2 | semidirect |
| 7. Dic23⋊C8 | C2 | semidirect |
| 27. D4×C23 | D4 | semidirect |
| 53. Dic23 | D8 | semidirect |
| 62. C2×D8 | D23 | semidirect |
| 68. C23 | #459 | semidirect |
| 92. D4 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×C23 | 2 |
| #10625111 | 2 |
| D4×Dic23 | 2 |
| C2×#67272 | 2 |
| #10625014 | 2 |
| #10625003 | 2 |
| Dic23⋊C8 | 2 |
| #459 | 23 |