Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊C4×D97 |
| commutator | C22×C97 | C22×C4 |
| Frattini | C23 | C22×D97 |
| Fitting | #99×C97 | C2 |
| socle | C2×C97 | C2×C22⋊C4 |
| hypercenter | #99 | D97 |
| hypocenter | C97 | C2×#99 |
| LCS | G ▷ C22×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #99 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22⋊C4×D97 | C2 | semidirect |
| 3. #15690725 | C2 | semidirect |
| 4. #15690724 | C2 | semidirect |
| 5. #99×C97 | C2 | semidirect |
| 6. C23×D97 | C4 | semidirect |
| 8. C2×D388 | C4 | semidirect |
| 9. C2×C22⋊D97 | C4 | semidirect |
| 14. C2×C4×D97 | C4 | semidirect |
| 15. C22⋊Dic97 | C22 | semidirect |
| 18. C22⋊C4×C97 | C22 | semidirect |
| 19. C23×C97 | C2×C4 | semidirect |
| 27. C22×D97 | C2×C4 | semidirect |
| 32. C2×C4×C97 | C2×C4 | semidirect |
| 36. C2×Dic97 | C2×C4 | semidirect |
| 68. D97 | #99 | direct (N × H) |
| 69. C97 | C2×#99 | semidirect |
| 75. #99 | D97 | direct (N × H) |
| 88. C22⋊C4 | C2×D97 | semidirect |
| 98. C23 | C4×D97 | semidirect |
| 110. C2×C4 | C4×D97 | semidirect |