Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
682 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 682 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, socle | C23×C37 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C37 |
| prime radical | C37×#2679 | C2 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ C2×C42×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C37×#2093 | C2 | semidirect |
| 3. C37×#2071 | C2 | semidirect |
| 4. C37×#1270 | C2 | semidirect |
| 5. C37×#1270 | C2 | semidirect |
| 15. C37×#384 | C22 | semidirect |
| 17. C37×#336 | C22 | semidirect |
| 18. C37×#336 | C22 | semidirect |
| 131. #7786 | C37 | direct (N × H) |
| 158. #2093 | C2×C37 | semidirect |
| 159. #2071 | C2×C37 | semidirect |
| 160. #1270 | C2×C37 | semidirect |
| 161. #1270 | C2×C37 | semidirect |
| 178. #384 | C22×C37 | semidirect |
| 180. #336 | C22×C37 | semidirect |
| 181. #336 | C22×C37 | semidirect |
| 182. C37 | #7786 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#2679 | 2 |
| C37×#2093 | 2 |
| C37×#2071 | 2 |
| C37×#1270 | 2 |
| #7786 | 37 |