Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
216 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 3. #23758192 | C2 | direct (N × H) |
| 77. C2×C157 | #362 | semidirect |
| 81. C157 | C2×#362 | semidirect |
| 161. C2 | #23758192 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097846 | 2 |
| C2×#19097841 | 2 |
| #23758192 | 2 |
| C2×Q16×D157 | 2 |
| C2×#362 | 157 |