Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 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. C2×#19097696 | C2 | semidirect |
| 4. #23757179 | C2 | semidirect |
| 6. #23757036 | C2 | semidirect |
| 7. C2×C4⋊C8×C157 | C2 | semidirect |
| 89. C2×C4×C157 | SD16 | semidirect |
| 129. C157 | #2055 | semidirect |
| 132. C2×C4⋊C8 | D157 | semidirect |
| 219. C2×C4 | #14578943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578943 | 2 |
| C2×#19097696 | 2 |
| C2×#19097693 | 2 |
| #23757179 | 2 |
| #23757175 | 2 |
| #23757036 | 2 |
| C2×C4⋊C8×C157 | 2 |
| #2055 | 157 |