Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
572 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 288 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×#6157 |
| commutator | C2×C53 | C22×C42 |
| Frattini | C22 | C23×#6157 |
| Fitting | C4×Q8×C53 | C4 |
| socle | C22×C53 | C23×C4 |
| hypercenter | C4×Q8 | #6157 |
| hypocenter | C53 | C4×#131 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16811588 | C2 | semidirect |
| 3. C4×#11719936 | C2 | semidirect |
| 4. C4×D53⋊C8 | C2 | semidirect |
| 6. #13133305 | C4 | direct (N × H) |
| 28. #11719936 | C2×C4 | semidirect |
| 29. D53⋊C8 | C2×C4 | semidirect |
| 57. C4×C53 | #131 | semidirect |
| 59. Dic53 | #131 | semidirect |
| 71. C53 | C4×#131 | semidirect |
| 126. C4 | #13133305 | direct (N × H) |