Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
399 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 399 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
| 268. A4 | #7333 | semidirect |
| 309. C22 | #10682523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#1313 | 2 |
| #72342686 | 2 |
| #72217184 | 3 |
| #10682523 | 4 |