Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
2818 conjugacy classes of subgroups; only the 374 normal subgroups are shown.
This group has 2818 conjugacy classes of subgroups — too many to draw. Only its 374 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C37 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C37 |
| prime radical | C26×C37 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C37×#397 | C2 | semidirect |
| 3. C37×#1439 | C2 | semidirect |
| 4. C37×#1437 | C2 | semidirect |
| 5. C37×#1437 | C2 | semidirect |
| 7. C22×C4⋊C4×C37 | C22 | semidirect |
| 12. C22×C42×C37 | C22 | semidirect |
| 15. C2×#95×C37 | C22 | semidirect |
| 16. C2×#95×C37 | C22 | semidirect |
| 17. C2×#95×C37 | C22 | semidirect |
| 140. #15480 | C37 | direct (N × H) |
| 165. C2×#397 | C2×C37 | semidirect |
| 167. #1439 | C2×C37 | semidirect |
| 168. #1437 | C2×C37 | semidirect |
| 169. #1437 | C2×C37 | semidirect |
| 177. C22×C4⋊C4 | C22×C37 | semidirect |
| 182. C22×C42 | C22×C37 | semidirect |
| 185. C2×#95 | C22×C37 | semidirect |
| 186. C2×#95 | C22×C37 | semidirect |
| 187. C2×#95 | C22×C37 | semidirect |
| 188. C37 | #15480 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C37×#397 | 2 |
| C2×C37×#379 | 2 |
| C37×#1439 | 2 |
| C37×#1437 | 2 |
| #15480 | 37 |