Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
396 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | #1519 |
| commutator | C2×C8 | C22×C4×C37 |
| Frattini, cosocle | C2×M16 | C23×C37 |
| prime radical | C37×#3058 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C2×C4×C37 ◁ C2×#131×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C37×#2115 | C2 | semidirect |
| 3. C37×#1812 | C2 | semidirect |
| 4. C37×#1339 | C2 | semidirect |
| 5. C22×D8×C37 | C4 | semidirect |
| 9. C37×#469 | C4 | semidirect |
| 14. C37×#427 | C4 | semidirect |
| 18. C37×#349 | C22 | semidirect |
| 19. C37×H(3,ℤ/4) | C22 | semidirect |
| 126. #11868 | C37 | direct (N × H) |
| 146. #2115 | C2×C37 | semidirect |
| 147. #1812 | C2×C37 | semidirect |
| 148. #1339 | C2×C37 | semidirect |
| 155. C22×D8 | C4×C37 | semidirect |
| 159. #469 | C4×C37 | semidirect |
| 164. #427 | C4×C37 | semidirect |
| 168. #349 | C22×C37 | semidirect |
| 169. H(3,ℤ/4) | C22×C37 | semidirect |
| 170. C37 | #11868 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#3058 | 2 |
| C37×#2115 | 2 |
| C37×#1812 | 2 |
| C37×#1339 | 2 |
| #11868 | 37 |