Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D113 |
| commutator | C4×C113 | C24 |
| Frattini | C4 | C23×D113 |
| Fitting | #137×C113 | C2 |
| socle | C2×C113 | C22×D4 |
| hypercenter | #137 | D113 |
| hypocenter | C113 | C2×#137 |
| LCS | G ▷ C4×C113 ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #137 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×D113 | C2 | semidirect |
| 3. #16813655 | C2 | semidirect |
| 4. #16813654 | C2 | semidirect |
| 5. #16813653 | C2 | semidirect |
| 6. #16813652 | C2 | semidirect |
| 7. #16813651 | C2 | semidirect |
| 8. Q16×D113 | C2 | semidirect |
| 9. SD16×D113 | C2 | semidirect |
| 10. M16×D113 | C2 | semidirect |
| 11. #137×C113 | C2 | semidirect |
| 18. C2×Dic226 | C22 | semidirect |
| 23. Q8×D113 | C22 | semidirect |
| 29. Dic452 | C22 | semidirect |
| 30. #14268637 | C22 | semidirect |
| 31. #14268637 | C22 | semidirect |
| 32. #14268636 | C22 | semidirect |
| 33. #14268635 | C22 | semidirect |
| 34. #14268634 | C22 | semidirect |
| 35. #14268631 | C22 | semidirect |
| 36. #14268630 | C22 | semidirect |
| 39. C2×Q8×C113 | C22 | semidirect |
| 40. Q16×C113 | C22 | semidirect |
| 41. SD16×C113 | C22 | semidirect |
| 42. M16×C113 | C22 | semidirect |
| 98. D113 | #137 | direct (N × H) |
| 99. C113 | C2×#137 | semidirect |
| 108. #137 | D113 | direct (N × H) |
| 125. C2×Q8 | C2×D113 | semidirect |
| 134. Q16 | C2×D113 | semidirect |
| 138. SD16 | C2×D113 | semidirect |
| 141. M16 | C2×D113 | semidirect |