Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 173 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. #23757560 | C2 | direct (N × H) |
| 3. C2×#19097702 | C2 | semidirect |
| 4. C2×C4⋊#11929434 | C2 | semidirect |
| 6. C2×C4⋊Q8×C157 | C2 | semidirect |
| 14. #19097702 | C22 | semidirect |
| 15. C4⋊#11929434 | C22 | semidirect |
| 19. C4⋊Q8×C157 | C22 | semidirect |
| 26. C2×D628 | Q8 | semidirect |
| 53. D628 | C2×Q8 | semidirect |
| 85. C2×C157 | #476 | semidirect |
| 90. C157 | C2×#476 | semidirect |
| 92. C2×C4⋊Q8 | D157 | semidirect |
| 103. C4⋊Q8 | C2×D157 | semidirect |
| 177. C2 | #23757560 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D628 | 2 |
| #23757560 | 2 |
| C2×#19097702 | 2 |
| C2×C4⋊#11929434 | 2 |
| C2×#19097691 | 2 |
| C2×C4⋊Q8×C157 | 2 |
| C2×#476 | 157 |