Finite Group DatabasebetaFinite Group Databasebeta← C4×ΓL(1,𝔽8)×#63271 #37524691
Order 22932.
168 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|
| C2×ΓL(1,𝔽8)×#63271 | 2 |
| C4×C13⋊#3862 | 3 |
| C4×#14274262 | 3 |
| C4×C7×#63271 | 3 |
| C4×C7×C13×ΓL(1,𝔽8) | 3 |
| C3×C4×#63271 | 7 |
| C4×ΓL(1,𝔽8)×C13⋊C3 | 7 |
| C4×ΓL(1,𝔽8)2 | 13 |