Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
294 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#89137 |
| commutator, socle | C2×C109 | C23×C4 |
| Fitting | #41×C109 | C4 |
| hypercenter | #41 | #89137 |
| hypocenter | C109 | #520 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#89137 | C2 | semidirect |
| 2. D4×#89137 | C2 | semidirect |
| 3. #16812778 | C2 | semidirect |
| 4. C2×C4⋊#89137 | C2 | semidirect |
| 12. #13182030 | C4 | semidirect |
| 13. #13182029 | C4 | semidirect |
| 14. #13182028 | C4 | semidirect |
| 18. #41×C109 | C4 | semidirect |
| 23. Q8×C109 | C2×C4 | semidirect |
| 24. D4×C109 | C2×C4 | semidirect |
| 25. C2×C4×C109 | C2×C4 | semidirect |
| 26. C22⋊D109 | C2×C4 | semidirect |
| 27. C2×Dic109 | C2×C4 | semidirect |
| 28. D436 | C2×C4 | semidirect |
| 29. C4×D109 | C2×C4 | semidirect |
| 30. C4×D109 | C2×C4 | semidirect |
| 33. Dic218 | C2×C4 | semidirect |
| 50. C109 | #520 | semidirect |
| 60. #41 | #89137 | semidirect |
| 72. Q8 | C2×#89137 | semidirect |
| 75. D4 | C2×#89137 | semidirect |
| 84. C2×C4 | C2×#89137 | semidirect |