Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
310 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 109 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 | #121×C107 | C2 |
| hypercenter | #121 | D107 |
| hypocenter | C107 | #532 |
| LCS | G ▷ C22×C107 ▷ C107 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133817 | C2 | semidirect |
| 2. #16812108 | C2 | semidirect |
| 3. #16812105 | C2 | semidirect |
| 4. #16812095 | C2 | semidirect |
| 5. #16812083 | C2 | semidirect |
| 6. #16812081 | C2 | semidirect |
| 7. D4×Dic107 | C2 | semidirect |
| 8. #16812071 | C2 | semidirect |
| 9. (C22⋊D107)⋊C4 | C2 | semidirect |
| 10. C2×C4×Dic107 | C2 | semidirect |
| 11. #121×C107 | C2 | semidirect |
| 50. C2×Dic107 | D4 | semidirect |
| 71. C4×C107 | #41 | semidirect |
| 76. Dic107 | #41 | semidirect |
| 83. C107 | #532 | semidirect |
| 91. #121 | D107 | semidirect |
| 160. C4 | #13133817 | semidirect |