Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×D97 |
| commutator, socle | C22×C97 | C24 |
| Fitting | C22⋊Q8×C97 | C2 |
| hypercenter | C22⋊Q8 | D97 |
| hypocenter | C97 | #525 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13095512 | C2 | semidirect |
| 2. C22×C4×D97 | C2 | semidirect |
| 3. #15690795 | C2 | semidirect |
| 4. #15690786 | C2 | semidirect |
| 5. #15690785 | C2 | semidirect |
| 6. #15690784 | C2 | semidirect |
| 7. #15690780 | C2 | semidirect |
| 8. #15690772 | C2 | semidirect |
| 9. #15690770 | C2 | semidirect |
| 10. #15690768 | C2 | semidirect |
| 11. C22⋊Q8×C97 | C2 | semidirect |
| 16. C2×D388 | C22 | semidirect |
| 24. C2×C4×D97 | C22 | semidirect |
| 25. C4⋊Dic97 | C22 | semidirect |
| 26. #13095490 | C22 | semidirect |
| 29. #13095488 | C22 | semidirect |
| 30. #13095488 | C22 | semidirect |
| 31. C4×Dic97 | C22 | semidirect |
| 32. C2×Q8×C97 | C22 | semidirect |
| 34. C4⋊C4×C97 | C22 | semidirect |
| 35. C4⋊C4×C97 | C22 | semidirect |
| 62. C4×D97 | D4 | semidirect |
| 65. C22×C97 | #41 | semidirect |
| 76. C2×D97 | #41 | semidirect |
| 91. C97 | #525 | semidirect |
| 97. C22⋊Q8 | D97 | semidirect |
| 106. C2×Q8 | C2×D97 | semidirect |
| 121. C4⋊C4 | C2×D97 | semidirect |
| 122. C4⋊C4 | C2×D97 | semidirect |
| 167. C22 | #13095512 | semidirect |