Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
1482 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 298 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 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C37 |
| prime radical | C2×H(5,𝔽2)×C37 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C37×#2486 | C2 | semidirect |
| 4. C37×#1890 | C2 | semidirect |
| 5. C37×#1799 | C2 | semidirect |
| 14. C22×C4⋊C4×C37 | C22 | semidirect |
| 20. C37×#381 | C22 | semidirect |
| 22. C37×#380 | C22 | semidirect |
| 23. C37×#342 | C22 | semidirect |
| 149. #32927 | C37 | direct (N × H) |
| 169. C4×C37 | #458 | semidirect |
| 172. #2486 | C2×C37 | semidirect |
| 173. #1890 | C2×C37 | semidirect |
| 174. #1799 | C2×C37 | semidirect |
| 189. C22×C4⋊C4 | C22×C37 | semidirect |
| 195. #381 | C22×C37 | semidirect |
| 197. #380 | C22×C37 | semidirect |
| 198. #342 | C22×C37 | semidirect |
| 199. C37 | #32927 | direct (N × H) |
| 344. C4 | C37×#458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×H(5,𝔽2)×C37 | 2 |
| C2×C37×#458 | 2 |
| C37×#2486 | 2 |
| C37×#1890 | 2 |
| C37×#1799 | 2 |
| #32927 | 37 |