Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
302 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23757313 | C2 | semidirect |
| 4. #23757142 | C2 | semidirect |
| 5. #23757041 | C2 | semidirect |
| 6. #23757034 | C2 | semidirect |
| 20. #19097698 | C4 | semidirect |
| 30. #14578938 | C2×C4 | semidirect |
| 43. C4×Dic157 | C2×C4 | semidirect |
| 71. Q8×C157 | C4⋊C4 | semidirect |
| 75. D4×C157 | C4⋊C4 | semidirect |
| 112. C157 | #1859 | semidirect |
| 175. Q8 | #14578933 | semidirect |
| 179. D4 | #14578933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757756 | 2 |
| #23757313 | 2 |
| C2×#19097698 | 2 |
| #23757142 | 2 |
| #23757041 | 2 |
| #23757034 | 2 |
| #417×C157 | 2 |
| #1859 | 157 |