Finite Group DatabasebetaFinite Group DatabasebetaOrder 6976.
120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#89137 |
| commutator | C4×C109 | C22×C4 |
| Frattini | C4 | C22×#89137 |
| Fitting | SD16×C109 | C4 |
| socle | C2×C109 | C4×D4 |
| hypercenter | SD16 | #89137 |
| hypocenter | C109 | #440 |
| LCS | G ▷ C4×C109 ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#89137 | C2 | semidirect |
| 3. #16812768 | C2 | semidirect |
| 4. #16812762 | C2 | semidirect |
| 6. #16812753 | C2 | semidirect |
| 18. #13182018 | C4 | semidirect |
| 19. #13182017 | C4 | semidirect |
| 20. #13182016 | C4 | semidirect |
| 22. SD16×C109 | C4 | semidirect |
| 29. Q8×C109 | C2×C4 | semidirect |
| 36. Dic218 | C2×C4 | semidirect |
| 38. C8×C109 | C2×C4 | semidirect |
| 39. #11724784 | C2×C4 | semidirect |
| 58. C109 | #440 | semidirect |
| 73. SD16 | #89137 | semidirect |
| 85. Q8 | C2×#89137 | semidirect |
| 98. C8 | C2×#89137 | semidirect |