Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
342 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D109 |
| commutator | C22×C109 | C24 |
| Frattini | C22 | C23×D109 |
| Fitting | C2×C4⋊C4×C109 | C2 |
| socle | C23×C109 | C23 |
| hypercenter | C2×C4⋊C4 | D109 |
| hypocenter | C109 | C2×#123 |
| 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. C22×C4×D109 | C2 | semidirect |
| 3. #16812684 | C2 | direct (N × H) |
| 4. C2×#13182008 | C2 | semidirect |
| 5. C2×#13182006 | C2 | semidirect |
| 6. C2×#13182006 | C2 | semidirect |
| 7. C2×#13182006 | C2 | semidirect |
| 8. C2×C4⋊C4×C109 | C2 | semidirect |
| 16. C2×C4×D109 | C22 | semidirect |
| 17. #13182008 | C22 | semidirect |
| 18. #13182006 | C22 | semidirect |
| 19. #13182006 | C22 | semidirect |
| 20. #13182006 | C22 | semidirect |
| 24. C4⋊C4×C109 | C22 | semidirect |
| 63. C2×C109 | #123 | semidirect |
| 69. C109 | C2×#123 | semidirect |
| 75. C2×C4⋊C4 | D109 | semidirect |
| 91. C4⋊C4 | C2×D109 | semidirect |
| 135. C2 | #16812684 | direct (N × H) |