Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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×Dic46 | C2 | semidirect |
| 3. C2×C4⋊C4×C23 | C2 | semidirect |
| 5. C2×C4⋊Dic23 | C2 | semidirect |
| 6. #10625068 | C2 | direct (N × H) |
| 15. C2×Dic46 | C22 | semidirect |
| 16. C4⋊C4×C23 | C22 | semidirect |
| 18. C4⋊Dic23 | C22 | semidirect |
| 22. C22×D23 | Q8 | semidirect |
| 41. C2×D23 | C2×Q8 | semidirect |
| 47. C2×C23 | C22⋊Q8 | semidirect |
| 56. C2×C4⋊C4 | D23 | semidirect |
| 58. C23 | C2×C22⋊Q8 | semidirect |
| 69. C4⋊C4 | C2×D23 | semidirect |
| 99. C2 | #10625068 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D23 | 2 |
| C22×Dic46 | 2 |
| C2×C4⋊C4×C23 | 2 |
| C2×(C2×D23)⋊C4 | 2 |
| C2×C4⋊Dic23 | 2 |
| #10625068 | 2 |
| C2×C22⋊Q8 | 23 |