Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D109 |
| commutator | C22×C109 | C22×C4 |
| Fitting | C2×C4⋊C4×C109 | C2 |
| socle | C23×C109 | C23 |
| hypercenter | C2×C4⋊C4 | D109 |
| hypocenter | C109 | #385 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13182008 | C2 | semidirect |
| 5. #16812606 | C2 | semidirect |
| 6. #16812606 | C2 | semidirect |
| 7. C2×C4⋊C4×C109 | C2 | semidirect |
| 17. #13182006 | C4 | semidirect |
| 37. C2×C4×C109 | C2×C4 | semidirect |
| 46. C2×Dic109 | C2×C4 | semidirect |
| 62. C2×D109 | C4⋊C4 | semidirect |
| 77. C109 | #385 | semidirect |
| 81. C2×C4⋊C4 | D109 | semidirect |
| 125. C2×C4 | C4×D109 | semidirect |