Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
411 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 411 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. C22×#7333 | C3 | semidirect |
| 24. A4×C32 | C8 | semidirect |
| 47. #7333 | A4 | direct (N × H) |
| 72. C22×C32 | C3×C8 | semidirect |
| 217. C32 | C8×A4 | semidirect |
| 269. A4 | #7333 | direct (N × H) |
| 310. C22 | C3×#7333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#1313 | 2 |
| A4×#1398 | 2 |
| C22×#7333 | 3 |
| C3×#7333 | 4 |