Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
294 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#87604 |
| commutator, socle | C2×C97 | C23×C4 |
| Fitting | #41×C97 | C4 |
| hypercenter | #41 | #87604 |
| hypocenter | C97 | #520 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#87604 | C2 | semidirect |
| 2. D4×#87604 | C2 | semidirect |
| 3. #15690889 | C2 | semidirect |
| 4. C2×C4⋊#87604 | C2 | semidirect |
| 12. #13095512 | C4 | semidirect |
| 13. #13095511 | C4 | semidirect |
| 14. #13095510 | C4 | semidirect |
| 18. #41×C97 | C4 | semidirect |
| 23. Q8×C97 | C2×C4 | semidirect |
| 24. D4×C97 | C2×C4 | semidirect |
| 25. C2×C4×C97 | C2×C4 | semidirect |
| 26. C22⋊D97 | C2×C4 | semidirect |
| 27. C2×Dic97 | C2×C4 | semidirect |
| 28. D388 | C2×C4 | semidirect |
| 29. C4×D97 | C2×C4 | semidirect |
| 30. C4×D97 | C2×C4 | semidirect |
| 33. Dic194 | C2×C4 | semidirect |
| 50. C97 | #520 | semidirect |
| 60. #41 | #87604 | semidirect |
| 72. Q8 | C2×#87604 | semidirect |
| 75. D4 | C2×#87604 | semidirect |
| 84. C2×C4 | C2×#87604 | semidirect |