Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23757683 | C2 | semidirect |
| 4. #23757682 | C2 | semidirect |
| 5. #23757679 | C2 | semidirect |
| 6. #23757677 | C2 | semidirect |
| 7. #23757670 | C2 | semidirect |
| 11. #501×C157 | C2 | semidirect |
| 52. #14578937 | Q8 | semidirect |
| 95. #11929434 | C2×Q8 | semidirect |
| 103. C8×C157 | C2×Q8 | semidirect |
| 124. C157 | #3165 | semidirect |
| 131. #501 | D157 | semidirect |
| 228. C8 | Q8×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757829 | 2 |
| C4⋊Q8×D157 | 2 |
| #23757683 | 2 |
| #23757682 | 2 |
| #23757679 | 2 |
| #23757677 | 2 |
| #23757670 | 2 |
| #23757314 | 2 |
| #23757312 | 2 |
| #23757225 | 2 |
| #501×C157 | 2 |
| #3165 | 157 |