Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
266 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22×D109 |
| commutator, socle | C2×C109 | C23×C4 |
| Frattini | C4 | C23×D109 |
| Fitting | #131×C109 | C2 |
| hypercenter | #131 | D109 |
| hypocenter | C109 | C2×#131 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C8 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16812707 | C2 | semidirect |
| 3. #16812706 | C2 | semidirect |
| 4. #16812705 | C2 | semidirect |
| 5. M16×D109 | C2 | semidirect |
| 6. C2×C8×D109 | C2 | semidirect |
| 7. #131×C109 | C2 | semidirect |
| 14. #13182013 | C22 | semidirect |
| 15. #13182012 | C22 | semidirect |
| 16. C2×#11724784 | C22 | semidirect |
| 19. C8×D109 | C22 | semidirect |
| 20. C8×D109 | C22 | semidirect |
| 22. M16×C109 | C22 | semidirect |
| 23. C2×C8×C109 | C22 | semidirect |
| 51. D109 | #131 | direct (N × H) |
| 52. C109 | C2×#131 | semidirect |
| 58. #131 | D109 | direct (N × H) |
| 70. M16 | C2×D109 | semidirect |
| 76. C2×C8 | C2×D109 | semidirect |