Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
210 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C157 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C157 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C157 ◁ C2×C4×C157 ◁ #131×C157 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #578×C157 | C2 | semidirect |
| 2. #509×C157 | C2 | semidirect |
| 3. C2×SD32×C157 | C2 | semidirect |
| 4. #472×C157 | C2 | semidirect |
| 5. #362×C157 | C2 | semidirect |
| 6. #359×C157 | C2 | semidirect |
| 7. #350×C157 | C2 | semidirect |
| 90. C157 | #2193 | direct (N × H) |
| 91. #2193 | C157 | direct (N × H) |
| 92. #578 | C2×C157 | semidirect |
| 93. #509 | C2×C157 | semidirect |
| 94. C2×SD32 | C2×C157 | semidirect |
| 95. #472 | C2×C157 | semidirect |
| 96. #362 | C2×C157 | semidirect |
| 97. #359 | C2×C157 | semidirect |
| 98. #350 | C2×C157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #578×C157 | 2 |
| #509×C157 | 2 |
| C2×SD32×C157 | 2 |
| #472×C157 | 2 |
| #362×C157 | 2 |
| #359×C157 | 2 |
| #350×C157 | 2 |
| #2193 | 157 |