Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
298 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D107 |
| commutator | C2×C107 | C23×C4 |
| Frattini | C4 | C23×D107 |
| Fitting | C2×M16×C107 | C2 |
| socle | C22×C107 | C22×C4 |
| hypercenter | C2×M16 | D107 |
| hypocenter | C107 | C22×M16 |
| LCS | G ▷ C2×C107 ▷ C107 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13133802 | C2 | semidirect |
| 3. C2×#13133801 | C2 | semidirect |
| 4. M16×D107 | C2 | direct (N × H) |
| 5. C2×C8×D107 | C2 | semidirect |
| 6. C2×M16×C107 | C2 | semidirect |
| 15. #13133802 | C22 | semidirect |
| 16. #13133801 | C22 | semidirect |
| 17. C2×C107⋊C8 | C22 | semidirect |
| 18. C8×D107 | C22 | semidirect |
| 20. M16×C107 | C22 | semidirect |
| 21. C2×C8×C107 | C22 | semidirect |
| 40. C8×C107 | C23 | semidirect |
| 41. C107⋊C8 | C23 | semidirect |
| 47. C2×D107 | M16 | direct (N × H) |
| 56. C2×C107 | C2×M16 | semidirect |
| 59. D107 | C2×M16 | direct (N × H) |
| 60. C107 | C22×M16 | semidirect |
| 66. C2×M16 | D107 | direct (N × H) |
| 79. M16 | C2×D107 | direct (N × H) |
| 82. C2×C8 | C2×D107 | semidirect |
| 102. C8 | C22×D107 | semidirect |
| 119. C2 | M16×D107 | direct (N × H) |