Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. C22×#14578941 | C2 | semidirect |
| 3. C2×#19097695 | C2 | semidirect |
| 4. C2×#19097691 | C2 | semidirect |
| 5. C2×C22⋊#11929434 | C2 | semidirect |
| 6. #23757035 | C2 | semidirect |
| 7. C2×C22⋊Q8×C157 | C2 | semidirect |
| 46. C2×#11929434 | D4 | semidirect |
| 56. C2×Q8×C157 | D4 | semidirect |
| 69. C4⋊C4×C157 | D4 | semidirect |
| 94. C23×C157 | SD16 | semidirect |
| 157. C157 | #2000 | semidirect |
| 160. C2×C22⋊Q8 | D157 | semidirect |
| 194. C2×Q8 | C22⋊D157 | semidirect |
| 226. C4⋊C4 | C22⋊D157 | semidirect |
| 242. C23 | #14578941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578941 | 2 |
| C2×#19097745 | 2 |
| C2×#19097695 | 2 |
| C2×#19097691 | 2 |
| C2×C22⋊#11929434 | 2 |
| #23757035 | 2 |
| C2×C22⋊Q8×C157 | 2 |
| #2000 | 157 |