Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23757350 | C2 | semidirect |
| 3. D4×#11929434 | C2 | semidirect |
| 4. #23757023 | C2 | semidirect |
| 5. #23757002 | C2 | semidirect |
| 6. #23756994 | C2 | semidirect |
| 7. D4⋊C8×C157 | C2 | semidirect |
| 55. D4×C157 | M16 | semidirect |
| 83. C157 | #1586 | semidirect |
| 90. D4⋊C8 | D157 | semidirect |
| 131. D4 | #14578937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14578939 | 2 |
| #23757350 | 2 |
| D4×#11929434 | 2 |
| #23757023 | 2 |
| #23757002 | 2 |
| #23756994 | 2 |
| D4⋊C8×C157 | 2 |
| #1586 | 157 |