Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 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 | C2×C22⋊Q8 |
| 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×Q8×D97 | C2 | semidirect |
| 3. #15690790 | C2 | semidirect |
| 4. #15690789 | C2 | semidirect |
| 5. #15690788 | C2 | semidirect |
| 6. #15690787 | C2 | semidirect |
| 7. #15690786 | C2 | semidirect |
| 8. C4⋊C4×D97 | C2 | semidirect |
| 9. C4⋊C4×D97 | C2 | semidirect |
| 11. C22⋊Q8×C97 | C2 | semidirect |
| 13. C2×Dic194 | C22 | semidirect |
| 14. C2×Dic194 | C22 | semidirect |
| 24. C4⋊Dic97 | C22 | semidirect |
| 25. C4⋊Dic97 | C22 | semidirect |
| 26. #13095490 | C22 | semidirect |
| 27. #13095490 | C22 | semidirect |
| 28. #13095490 | C22 | semidirect |
| 32. C2×Q8×C97 | C22 | semidirect |
| 34. C4⋊C4×C97 | C22 | semidirect |
| 35. C4⋊C4×C97 | C22 | semidirect |
| 40. C22×D97 | Q8 | semidirect |
| 64. C22×C97 | C2×Q8 | semidirect |
| 71. C2×D97 | C2×Q8 | semidirect |
| 86. D97 | C22⋊Q8 | direct (N × H) |
| 87. C97 | C2×C22⋊Q8 | semidirect |
| 96. C22⋊Q8 | D97 | direct (N × H) |
| 104. C2×Q8 | C2×D97 | semidirect |
| 119. C4⋊C4 | C2×D97 | semidirect |
| 120. C4⋊C4 | C2×D97 | semidirect |
| 159. C22 | Q8×D97 | semidirect |