Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×C22⋊D109 |
| commutator | C4×C109 | C24 |
| Frattini | C4 | C23×D109 |
| Fitting | 2−1+4×C109 | C2 |
| socle | C2×C109 | C22×D4 |
| hypercenter | 2−1+4 | D109 |
| hypocenter | C109 | #577 |
| LCS | G ▷ C4×C109 ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ 2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16812745 | C2 | semidirect |
| 2. #16812730 | C2 | semidirect |
| 3. #16812724 | C2 | semidirect |
| 4. #16812719 | C2 | semidirect |
| 5. C2×#13182016 | C2 | semidirect |
| 6. #16812706 | C2 | semidirect |
| 7. 2−1+4×C109 | C2 | semidirect |
| 12. #13182019 | C22 | semidirect |
| 13. #13182017 | C22 | semidirect |
| 14. #13182016 | C22 | semidirect |
| 15. #13182016 | C22 | semidirect |
| 16. #13182014 | C22 | semidirect |
| 17. #13182013 | C22 | semidirect |
| 18. C2×#11724784 | C22 | semidirect |
| 21. #41×C109 | C22 | semidirect |
| 23. C2×Q8×C109 | C22 | semidirect |
| 53. C109 | #577 | semidirect |
| 55. 2−1+4 | D109 | semidirect |
| 66. #41 | C2×D109 | semidirect |
| 68. C2×Q8 | C2×D109 | semidirect |