Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23757754 | C2 | semidirect |
| 3. C2×#19097697 | C2 | semidirect |
| 4. #23757279 | C2 | semidirect |
| 5. #23757174 | C2 | semidirect |
| 6. #23757034 | C2 | semidirect |
| 7. #343×C157 | C2 | semidirect |
| 11. #19097799 | C4 | semidirect |
| 39. C2×D628 | C2×C4 | semidirect |
| 62. M16×C157 | C2×C4 | semidirect |
| 74. Dic314 | C22⋊C4 | semidirect |
| 80. D628 | C22⋊C4 | semidirect |
| 132. C157 | #1883 | semidirect |
| 139. #343 | D157 | semidirect |
| 185. M16 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097799 | 2 |
| #23757754 | 2 |
| C2×#19097697 | 2 |
| #23757279 | 2 |
| #23757174 | 2 |
| #23757034 | 2 |
| #343×C157 | 2 |
| #1883 | 157 |