Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
426 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×#89137 |
| commutator | C2×C109 | C23×C4 |
| Frattini | C2 | C23×#89137 |
| Fitting | C2×D4×C109 | C4 |
| socle | C22×C109 | C22×C4 |
| hypercenter | C2×D4 | #89137 |
| hypocenter | C109 | C2×C4×D4 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#89137 | C2 | semidirect |
| 2. D4×#89137 | C2 | direct (N × H) |
| 3. C2×C4⋊#89137 | C2 | semidirect |
| 4. C2×C22⋊#89137 | C2 | semidirect |
| 5. C2×C4×#89137 | C2 | semidirect |
| 11. C22×#89137 | C22 | semidirect |
| 12. C4⋊#89137 | C22 | semidirect |
| 13. C22⋊#89137 | C22 | semidirect |
| 14. C4×#89137 | C22 | semidirect |
| 16. C2×D436 | C4 | semidirect |
| 17. C2×C22⋊D109 | C4 | semidirect |
| 18. D4×D109 | C4 | semidirect |
| 21. C2×D4×C109 | C4 | semidirect |
| 22. C23×C109 | C2×C4 | semidirect |
| 25. C22×D109 | C2×C4 | semidirect |
| 26. C22×D109 | C2×C4 | semidirect |
| 32. C2×#89137 | D4 | direct (N × H) |
| 36. D4×C109 | C2×C4 | semidirect |
| 37. C2×C4×C109 | C2×C4 | semidirect |
| 38. C22⋊D109 | C2×C4 | semidirect |
| 39. C2×Dic109 | C2×C4 | semidirect |
| 40. D436 | C2×C4 | semidirect |
| 41. C4×D109 | C2×C4 | semidirect |
| 45. C22×C109 | C22×C4 | semidirect |
| 51. C2×D109 | C22×C4 | semidirect |
| 57. #89137 | C2×D4 | direct (N × H) |
| 58. C4×C109 | C22×C4 | semidirect |
| 59. Dic109 | C22×C4 | semidirect |
| 61. C2×C109 | C4×D4 | semidirect |
| 64. D109 | C4×D4 | semidirect |
| 67. C109 | C2×C4×D4 | semidirect |
| 80. C2×D4 | #89137 | direct (N × H) |
| 96. C23 | C2×#89137 | semidirect |
| 99. D4 | C2×#89137 | direct (N × H) |
| 110. C2×C4 | C2×#89137 | semidirect |
| 122. C22 | C22×#89137 | semidirect |
| 127. C4 | C22×#89137 | semidirect |
| 133. C2 | D4×#89137 | direct (N × H) |