Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 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. #23757996 | C2 | semidirect |
| 2. #23757983 | C2 | semidirect |
| 3. #23757628 | C2 | semidirect |
| 4. #23757624 | C2 | semidirect |
| 5. #23757581 | C2 | semidirect |
| 6. #23757564 | C2 | semidirect |
| 8. #23757479 | C2 | semidirect |
| 9. C4×#14578943 | C2 | semidirect |
| 11. C8×Q8×C157 | C2 | semidirect |
| 120. C157 | #3360 | semidirect |
| 130. C8×Q8 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757996 | 2 |
| #23757983 | 2 |
| #23757628 | 2 |
| #23757624 | 2 |
| #23757581 | 2 |
| #23757564 | 2 |
| #23757489 | 2 |
| #23757479 | 2 |
| C4×#14578943 | 2 |
| C4×D1256 | 2 |
| C8×Q8×C157 | 2 |
| #3360 | 157 |