Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
290 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D107 |
| commutator, socle | C22×C107 | C24 |
| Fitting | #124×C107 | C2 |
| hypercenter | #124 | D107 |
| hypocenter | C107 | #548 |
| LCS | G ▷ C22×C107 ▷ C107 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133817 | C2 | semidirect |
| 2. C2×Q8×D107 | C2 | semidirect |
| 3. #16812095 | C2 | semidirect |
| 4. #16812086 | C2 | semidirect |
| 5. #16812085 | C2 | semidirect |
| 6. #16812082 | C2 | semidirect |
| 7. #16812080 | C2 | semidirect |
| 8. C4×Dic214 | C2 | semidirect |
| 9. C4×D428 | C2 | semidirect |
| 10. (C22⋊D107)⋊C4 | C2 | semidirect |
| 11. #124×C107 | C2 | semidirect |
| 58. Dic214 | D4 | semidirect |
| 68. C2×D107 | #41 | semidirect |
| 83. C107 | #548 | semidirect |
| 88. #124 | D107 | semidirect |