Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
176 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C157 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C157 |
| prime radical | #459×C157 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C157 ◁ C42×C157 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #486×C157 | C2 | semidirect |
| 2. #476×C157 | C2 | semidirect |
| 4. C8×D4×C157 | C2 | semidirect |
| 5. #334×C157 | C2 | semidirect |
| 6. #333×C157 | C2 | semidirect |
| 7. #331×C157 | C2 | semidirect |
| 82. C157 | #1677 | direct (N × H) |
| 83. #1677 | C157 | direct (N × H) |
| 84. #486 | C2×C157 | semidirect |
| 85. #476 | C2×C157 | semidirect |
| 87. C8×D4 | C2×C157 | semidirect |
| 88. #334 | C2×C157 | semidirect |
| 89. #333 | C2×C157 | semidirect |
| 90. #331 | C2×C157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #486×C157 | 2 |
| #476×C157 | 2 |
| #459×C157 | 2 |
| C8×D4×C157 | 2 |
| #334×C157 | 2 |
| #333×C157 | 2 |
| #331×C157 | 2 |
| #1677 | 157 |