Finite Group DatabasebetaFinite Group DatabasebetaOrder 6174.
368 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C73 | C2×C32 |
| LCS | G ▷ C73 | |
| UCS | C1 | |
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 |
|---|---|
| #72228801 | 3 |
| #72228797 | 3 |
| #72228772 | 3 |
| #72228769 | 3 |
| ΓL(1,𝔽8)×#3861 | 2 |
| C3×#64424 | 7 |
| ΓL(1,𝔽8)⋊AGL(1,𝔽7) | 7 |