Finite Group DatabasebetaFinite Group DatabasebetaOrder 6592.
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | D4×D103 |
| commutator | C4×C103 | C24 |
| Frattini | C4 | C23×D103 |
| Fitting | #135×C103 | C2 |
| socle | C2×C103 | C22×D4 |
| hypercenter | #135 | D103 |
| hypocenter | C103 | #575 |
| LCS | G ▷ C4×C103 ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #135 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #41×D103 | C2 | semidirect |
| 2. #15693053 | C2 | semidirect |
| 3. #15693050 | C2 | semidirect |
| 4. #15693048 | C2 | semidirect |
| 5. #15693045 | C2 | semidirect |
| 6. #15693043 | C2 | semidirect |
| 7. #15693041 | C2 | semidirect |
| 8. C2×#13110088 | C2 | semidirect |
| 9. #135×C103 | C2 | semidirect |
| 12. #13110105 | C22 | semidirect |
| 15. Q8×D103 | C22 | semidirect |
| 17. D4×D103 | C22 | semidirect |
| 20. Dic412 | C22 | semidirect |
| 21. #13110095 | C22 | semidirect |
| 22. #13110094 | C22 | semidirect |
| 23. #13110093 | C22 | semidirect |
| 24. #13110092 | C22 | semidirect |
| 25. D824 | C22 | semidirect |
| 26. #13110090 | C22 | semidirect |
| 27. #13110088 | C22 | semidirect |
| 28. #13110088 | C22 | semidirect |
| 29. C2×C103⋊C8 | C22 | semidirect |
| 30. #41×C103 | C22 | semidirect |
| 31. Q16×C103 | C22 | semidirect |
| 32. SD16×C103 | C22 | semidirect |
| 33. D8×C103 | C22 | semidirect |
| 34. C2×C8×C103 | C22 | semidirect |
| 75. C103 | #575 | semidirect |
| 84. #135 | D103 | semidirect |
| 91. #41 | C2×D103 | semidirect |
| 99. Q16 | C2×D103 | semidirect |
| 103. SD16 | C2×D103 | semidirect |
| 106. D8 | C2×D103 | semidirect |
| 110. C2×C8 | C2×D103 | semidirect |