Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
762 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 238 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C37 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C37 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ C43×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 50. C42×C37 | Q16 | semidirect |
| 67. #32801 | C37 | direct (N × H) |
| 96. C37 | #32801 | direct (N × H) |
| 130. C42 | Q16×C37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#2868 | 2 |
| C37×#2863 | 2 |
| C37×#2043 | 2 |
| C37×#2016 | 2 |
| C37×#1839 | 2 |
| #32801 | 37 |