Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
691 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 691 conjugacy classes of subgroups — too many to draw. Only its 255 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D7×ΓL(1,𝔽8) |
| commutator, socle, cosocle | C2×C72 | C24×C3 |
| Fitting | C2×C72×D4 | C2×C3 |
| hypercenter | C2×D4 | D7×ΓL(1,𝔽8) |
| hypocenter | C72 | C3×H(5,𝔽2) |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
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 |
|---|---|
| D4×D7×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×#1159 | 2 |
| C2×ΓL(1,𝔽8)×C22⋊D7 | 2 |
| ΓL(1,𝔽8)×#1157 | 2 |
| C2×C7×D4×ΓL(1,𝔽8) | 2 |
| C7×#6548 | 3 |
| C3×#6548 | 7 |
| ΓL(1,𝔽8)×H(5,𝔽2) | 7 |