Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23758001 | C2 | semidirect |
| 3. #23757623 | C2 | semidirect |
| 4. #23757580 | C2 | semidirect |
| 7. #23757480 | C2 | semidirect |
| 8. Q8×#11929434 | C2 | semidirect |
| 9. C4×#14578944 | C2 | semidirect |
| 115. C157 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758001 | 2 |
| #23757627 | 2 |
| #23757623 | 2 |
| #23757580 | 2 |
| #23757553 | 2 |
| #23757492 | 2 |
| #23757480 | 2 |
| Q8×#11929434 | 2 |
| C4×#14578944 | 2 |
| C4×#14578942 | 2 |
| #556×C157 | 2 |
| #3364 | 157 |