Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 | #123×C109 | C2 |
| hypercenter | #123 | D109 |
| hypocenter | C109 | #547 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13182029 | C2 | semidirect |
| 2. C2×#13182028 | C2 | semidirect |
| 3. #16812698 | C2 | semidirect |
| 4. #16812684 | C2 | semidirect |
| 5. #16812683 | C2 | semidirect |
| 6. #16812681 | C2 | semidirect |
| 7. #16812677 | C2 | semidirect |
| 8. #16812676 | C2 | semidirect |
| 9. #16812672 | C2 | semidirect |
| 10. #16812671 | C2 | semidirect |
| 11. #16812659 | C2 | semidirect |
| 12. #16812659 | C2 | semidirect |
| 13. C2×#13182008 | C2 | semidirect |
| 14. C4⋊C4×D109 | C2 | semidirect |
| 15. #123×C109 | C2 | semidirect |
| 67. C22⋊D109 | D4 | semidirect |
| 107. Dic109 | #41 | semidirect |
| 115. C109 | #547 | semidirect |
| 123. #123 | D109 | semidirect |