Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×C22⋊D97 |
| commutator | C4×C97 | C24 |
| Frattini | C4 | C23×D97 |
| Fitting | C2×#41×C97 | C2 |
| socle | C2×C97 | C22×D4 |
| hypercenter | C2×#41 | D97 |
| hypocenter | C97 | #575 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13095511 | C2 | semidirect |
| 2. #15690841 | C2 | semidirect |
| 3. #15690840 | C2 | semidirect |
| 4. #15690836 | C2 | semidirect |
| 5. #15690835 | C2 | semidirect |
| 6. #15690830 | C2 | semidirect |
| 7. C2×#13095495 | C2 | semidirect |
| 8. C2×#41×C97 | C2 | semidirect |
| 12. #13095511 | C22 | semidirect |
| 13. C2×Dic194 | C22 | semidirect |
| 14. C2×D388 | C22 | semidirect |
| 17. #13095501 | C22 | semidirect |
| 18. #13095499 | C22 | semidirect |
| 19. #13095498 | C22 | semidirect |
| 20. #13095496 | C22 | semidirect |
| 21. #13095495 | C22 | semidirect |
| 22. #13095495 | C22 | semidirect |
| 23. C2×#11715895 | C22 | semidirect |
| 27. #41×C97 | C22 | semidirect |
| 28. C2×Q8×C97 | C22 | semidirect |
| 30. C2×D4×C97 | C22 | semidirect |
| 81. C97 | #575 | semidirect |
| 84. C2×#41 | D97 | semidirect |
| 98. #41 | C2×D97 | semidirect |
| 100. C2×Q8 | C2×D97 | semidirect |
| 104. C2×D4 | C2×D97 | semidirect |