Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
338 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#90673 |
| commutator, socle | C2×C113 | C23×C4 |
| Fitting | C2×D4×C113 | C4 |
| hypercenter | C2×D4 | #90673 |
| hypocenter | C113 | #518 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×#90673 | C2 | semidirect |
| 2. #16813701 | C2 | semidirect |
| 3. C2×C22⋊#90673 | C2 | semidirect |
| 5. C22×#90673 | C22 | semidirect |
| 6. C4⋊#90673 | C22 | semidirect |
| 8. C22⋊#90673 | C22 | semidirect |
| 9. C4×#90673 | C22 | semidirect |
| 11. C2×D452 | C4 | semidirect |
| 12. C2×C22⋊D113 | C4 | semidirect |
| 13. D4×D113 | C4 | semidirect |
| 16. C2×D4×C113 | C4 | semidirect |
| 17. C23×C113 | C2×C4 | semidirect |
| 19. C22×D113 | C2×C4 | semidirect |
| 20. C22×D113 | C2×C4 | semidirect |
| 25. D4×C113 | C2×C4 | semidirect |
| 26. C2×C4×C113 | C2×C4 | semidirect |
| 27. C22⋊D113 | C2×C4 | semidirect |
| 28. C2×Dic113 | C2×C4 | semidirect |
| 29. D452 | C2×C4 | semidirect |
| 30. C4×D113 | C2×C4 | semidirect |
| 51. C113 | #518 | semidirect |
| 62. C2×D4 | #90673 | semidirect |
| 74. C23 | C2×#90673 | semidirect |
| 77. D4 | C2×#90673 | semidirect |
| 83. C2×C4 | C2×#90673 | semidirect |