Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
238 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 97 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 | #553 |
| 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. #16812102 | C2 | semidirect |
| 2. #16812100 | C2 | semidirect |
| 3. #16812090 | C2 | semidirect |
| 4. #16812080 | C2 | semidirect |
| 5. #16812080 | C2 | semidirect |
| 6. D4×Dic107 | C2 | semidirect |
| 7. C4×C22⋊D107 | C2 | semidirect |
| 8. (C22⋊D107)⋊C4 | C2 | semidirect |
| 9. #16812068 | C2 | semidirect |
| 10. C4⋊C4×D107 | C2 | semidirect |
| 11. #121×C107 | C2 | semidirect |
| 78. C107 | #553 | semidirect |
| 85. #121 | D107 | semidirect |