Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
310 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 310 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×D109 |
| commutator, socle | C22×C109 | C24 |
| Fitting | #121×C109 | C2 |
| hypercenter | #121 | D109 |
| hypocenter | C109 | #532 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13182028 | C2 | semidirect |
| 2. #16812698 | C2 | semidirect |
| 3. #16812695 | C2 | semidirect |
| 4. #16812685 | C2 | semidirect |
| 5. #16812673 | C2 | semidirect |
| 6. #16812671 | C2 | semidirect |
| 7. D4×Dic109 | C2 | semidirect |
| 8. #16812661 | C2 | semidirect |
| 9. #16812659 | C2 | semidirect |
| 10. C2×C4×Dic109 | C2 | semidirect |
| 11. #121×C109 | C2 | semidirect |
| 50. C2×Dic109 | D4 | semidirect |
| 71. C4×C109 | #41 | semidirect |
| 76. Dic109 | #41 | semidirect |
| 83. C109 | #532 | semidirect |
| 91. #121 | D109 | semidirect |
| 160. C4 | #13182028 | semidirect |