Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
396 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 23. A4×C32 | C8 | semidirect |
| 66. C22×C32 | C3⋊C8 | semidirect |
| 214. C32 | A4⋊C8 | semidirect |
| 266. A4 | #7333 | semidirect |
| 307. C22 | #10682522 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72342703 | 2 |
| A4×#1398 | 2 |
| #72342686 | 2 |
| #72319345 | 3 |
| #10682522 | 4 |