Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
212 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C37 | #95 |
| commutator | C2×C4 | C4×C8×C37 |
| Frattini, cosocle | C2×C4×C8 | C22×C37 |
| socle | C22×C37 | #336 |
| prime radical | C23×C37 | C4⋊C8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C37 ◁ C2×C4×C8×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 66. #7164 | C37 | direct (N × H) |
| 96. C37 | #7164 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#2163 | 2 |
| C4×M32×C37 | 2 |
| C37×#1451 | 2 |
| #7164 | 37 |