Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
344 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 24. A4×C32 | C8 | semidirect |
| 70. C22×C32 | C3⋊C8 | semidirect |
| 223. C32 | A4⋊C8 | semidirect |
| 277. A4 | #7457 | semidirect |
| 318. C22 | #10682857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72342697 | 2 |
| #72342693 | 2 |
| A4×#1398 | 2 |
| #72319337 | 3 |
| #10682857 | 4 |