Finite Group DatabasebetaFinite Group DatabasebetaOrder 7056.
1620 conjugacy classes of subgroups; only the 456 normal subgroups are shown.
This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 456 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.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×#3861 | 2 |
| C3×D4×#3861 | 2 |
| C2×C3×C4×#3861 | 2 |
| C2×C3×C72×D4 | 3 |
| C2×D4×#3861 | 3 |
| C2×C3×D4×ΓL(1,𝔽8) | 7 |