Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D113 |
| commutator, socle | C22×C113 | C24 |
| Fitting | C2×#41×C113 | C2 |
| hypercenter | C2×#41 | D113 |
| hypocenter | C113 | #546 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×D113 | C2 | semidirect |
| 2. #16813611 | C2 | semidirect |
| 3. #16813605 | C2 | semidirect |
| 4. #16813598 | C2 | semidirect |
| 5. #16813596 | C2 | semidirect |
| 6. #16813594 | C2 | semidirect |
| 7. #16813590 | C2 | semidirect |
| 8. D4×Dic113 | C2 | semidirect |
| 9. C4×C22⋊D113 | C2 | semidirect |
| 10. C2×#14268624 | C2 | semidirect |
| 11. C2×#41×C113 | C2 | semidirect |
| 16. C2×C22⋊D113 | C22 | semidirect |
| 18. C22×Dic113 | C22 | semidirect |
| 20. C4⋊Dic113 | C22 | semidirect |
| 21. #14268626 | C22 | semidirect |
| 22. #14268626 | C22 | semidirect |
| 23. C22⋊Dic113 | C22 | semidirect |
| 24. C22⋊Dic113 | C22 | semidirect |
| 27. #14268624 | C22 | semidirect |
| 28. #14268624 | C22 | semidirect |
| 29. #14268624 | C22 | semidirect |
| 30. C4×Dic113 | C22 | semidirect |
| 32. C2×Q8×C113 | C22 | semidirect |
| 34. C2×D4×C113 | C22 | semidirect |
| 35. C22×C4×C113 | C22 | semidirect |
| 36. C22×C4×C113 | C22 | semidirect |
| 46. D4×C113 | D4 | semidirect |
| 75. C2×D113 | #41 | semidirect |
| 90. C113 | #546 | semidirect |
| 92. C2×#41 | D113 | semidirect |
| 105. C2×Q8 | C2×D113 | semidirect |
| 112. C2×D4 | C2×D113 | semidirect |
| 115. C22×C4 | C2×D113 | semidirect |
| 116. C22×C4 | C2×D113 | semidirect |
| 141. D4 | C22⋊D113 | semidirect |