Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
290 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C37 |
| prime radical | C37×#466 | C22 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C22×C4×C37 ◁ C37×#424 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C37×#2235 | C2 | semidirect |
| 4. C37×#2089 | C2 | semidirect |
| 5. C37×#1350 | C2 | semidirect |
| 7. C37×#1323 | C2 | semidirect |
| 121. #12295 | C37 | direct (N × H) |
| 139. #2235 | C2×C37 | semidirect |
| 141. #2089 | C2×C37 | semidirect |
| 142. #1350 | C2×C37 | semidirect |
| 144. #1323 | C2×C37 | semidirect |
| 169. C37 | #12295 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#3262 | 2 |
| C37×#2235 | 2 |
| C37×#2233 | 2 |
| C37×#2089 | 2 |
| C37×#1350 | 2 |
| C37×#1349 | 2 |
| C37×#1323 | 2 |
| #12295 | 37 |