Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
426 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D113 |
| commutator | C2×C113 | C23×C4 |
| Frattini | C22 | C23×D113 |
| Fitting | C2×C42×C113 | C2 |
| socle | C23×C113 | C23 |
| hypercenter | C2×C42 | D113 |
| hypocenter | C113 | C2×C4×D4 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C4×D113 | C2 | semidirect |
| 3. C4×D452 | C2 | direct (N × H) |
| 4. C2×C4⋊Dic113 | C2 | semidirect |
| 5. C2×#14268624 | C2 | semidirect |
| 6. C2×C42×C113 | C2 | semidirect |
| 8. C2×D452 | C4 | direct (N × H) |
| 12. C2×C4×D113 | C22 | semidirect |
| 13. C4⋊Dic113 | C22 | semidirect |
| 14. #14268624 | C22 | semidirect |
| 18. C42×C113 | C22 | semidirect |
| 22. C22×D113 | C2×C4 | semidirect |
| 25. C2×C4×C113 | C2×C4 | semidirect |
| 26. C2×C4×C113 | D4 | semidirect |
| 32. D452 | C2×C4 | direct (N × H) |
| 41. C2×D113 | C22×C4 | semidirect |
| 43. C4×C113 | C22×C4 | semidirect |
| 44. C4×C113 | C2×D4 | semidirect |
| 46. C2×C113 | C4×D4 | semidirect |
| 51. C113 | C2×C4×D4 | semidirect |
| 58. C2×C42 | D113 | semidirect |
| 70. C42 | C2×D113 | semidirect |
| 81. C2×C4 | C4×D113 | semidirect |
| 82. C2×C4 | D452 | direct (N × H) |
| 96. C4 | C2×C4×D113 | semidirect |
| 97. C4 | C2×D452 | direct (N × H) |
| 99. C2 | C4×D452 | direct (N × H) |