Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D107 |
| commutator, socle | C23×C107 | C23 |
| Fitting | C2×C22⋊C4×C107 | C2 |
| hypercenter | C2×C22⋊C4 | D107 |
| hypocenter | C107 | #393 |
| LCS | G ▷ C23×C107 ▷ C107 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic214 | C2 | semidirect |
| 3. C107⋊#95 | C2 | semidirect |
| 4. C107⋊#95 | C2 | semidirect |
| 19. C23×C107 | Q8 | semidirect |
| 52. C107 | #393 | semidirect |
| 72. C23 | Dic214 | semidirect |