Finite Group DatabasebetaFinite Group Databasebeta← AGL(1,𝔽7)×#11716321 #45692015
Order 33516.
248 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 56 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 | C72×C19 | C22×C32 |
| LCS | G ▷ C72×C19 | |
| 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 |
|---|---|
| ΓL(1,𝔽8)×#11716321 | 2 |
| AGL(1,𝔽7)×#87704 | 2 |
| ΓL(1,𝔽8)⋊#11716321 | 2 |
| D7×#11716321 | 3 |
| #26013909 | 3 |
| #26013905 | 3 |
| C7×D19×AGL(1,𝔽7) | 3 |
| C2×C3×#11716321 | 7 |
| AGL(1,𝔽7)×D19⋊C3 | 7 |
| C2×ΓL(1,𝔽8)×AGL(1,𝔽7) | 19 |