Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
238 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 97 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 | #117×C109 | C2 |
| hypercenter | #117 | D109 |
| hypocenter | C109 | #553 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16812693 | C2 | semidirect |
| 2. #16812690 | C2 | semidirect |
| 3. #16812681 | C2 | semidirect |
| 4. #16812674 | C2 | semidirect |
| 5. #16812673 | C2 | semidirect |
| 6. #16812672 | C2 | semidirect |
| 7. C4×D436 | C2 | semidirect |
| 8. #16812661 | C2 | semidirect |
| 9. C4×C22⋊D109 | C2 | semidirect |
| 10. C4⋊C4×D109 | C2 | semidirect |
| 11. #117×C109 | C2 | semidirect |
| 78. C109 | #553 | semidirect |
| 89. #117 | D109 | semidirect |