Finite Group DatabasebetaFinite Group DatabasebetaOrder 5312.
132 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×C22⋊D83 |
| commutator | C4×C83 | C22×C4 |
| Frattini | C2×C4 | C22×D83 |
| Fitting | C4×D4×C83 | C2 |
| socle | C22×C83 | C2×D4 |
| hypercenter | C4×D4 | D83 |
| hypocenter | C83 | #442 |
| LCS | G ▷ C4×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×D332 | C2 | semidirect |
| 3. #14581723 | C2 | semidirect |
| 4. #14581713 | C2 | semidirect |
| 5. #14581712 | C2 | semidirect |
| 6. #14581703 | C2 | semidirect |
| 7. C4×D4×C83 | C2 | semidirect |
| 10. #13050575 | C4 | semidirect |
| 23. D4×C83 | C2×C4 | semidirect |
| 31. D332 | C2×C4 | semidirect |
| 34. C83⋊C8 | C2×C4 | semidirect |
| 53. C83 | #442 | semidirect |
| 57. C4×D4 | D83 | semidirect |
| 79. D4 | C4×D83 | semidirect |