Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
200 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | C13⋊#3862 |
| commutator, cosocle, hypocenter | C72×C13 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C72×C13 | C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C22×C5 | |
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×C5×C13⋊#3862 | 2 |
| C22×C5×C72×C13 | 3 |
| C22×C13⋊#3862 | 5 |
| C22×C5×#63271 | 7 |
| C22×C5×#63270 | 7 |
| C22×C5×#3862 | 13 |