Finite Group DatabasebetaFinite Group DatabasebetaOrder 5312.
106 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D83 |
| commutator | C2×C4×C83 | C23 |
| Frattini | C2×C4 | C22×D83 |
| Fitting | #102×C83 | C2 |
| socle | C22×C83 | C2×D4 |
| hypercenter | #102 | D83 |
| hypocenter | C83 | #482 |
| LCS | G ▷ C2×C4×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #102 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14581750 | C2 | semidirect |
| 3. #14581725 | C2 | semidirect |
| 4. #14581724 | C2 | semidirect |
| 5. #14581713 | C2 | semidirect |
| 6. (C2×D83)⋊C8 | C2 | semidirect |
| 7. #102×C83 | C2 | semidirect |
| 51. C83 | #482 | semidirect |
| 58. #102 | D83 | semidirect |