Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
952 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 173 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 | C23×D53 |
| commutator, socle | C23×C53 | C24 |
| Fitting | C4×C22⋊C4×C53 | C2 |
| hypercenter | C4×C22⋊C4 | D53 |
| hypocenter | C53 | #2431 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11719945 | C2 | semidirect |
| 2. C2×#13133214 | C2 | semidirect |
| 3. C2×#13133205 | C2 | semidirect |
| 4. C2×#13133191 | C2 | semidirect |
| 5. #16810532 | C2 | semidirect |
| 6. #16810529 | C2 | semidirect |
| 7. #16810525 | C2 | semidirect |
| 8. #16810501 | C2 | semidirect |
| 9. C4×C22⋊C4×C53 | C2 | semidirect |
| 38. C22×C4×C53 | D4 | semidirect |
| 59. C2×D212 | D4 | semidirect |
| 65. C2×Dic106 | D4 | semidirect |
| 101. C2×C4×C53 | #41 | semidirect |
| 157. C4×C22⋊C4 | D53 | semidirect |
| 158. C53 | #2431 | semidirect |
| 210. C22×C4 | D212 | semidirect |
| 260. C2×C4 | #11719945 | semidirect |