Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23758008 | C2 | semidirect |
| 3. #23757474 | C2 | semidirect |
| 4. #23757473 | C2 | semidirect |
| 5. #23757016 | C2 | semidirect |
| 6. #23757005 | C2 | semidirect |
| 7. Q8⋊C8×C157 | C2 | semidirect |
| 98. C157 | #1620 | semidirect |
| 106. Q8⋊C8 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758008 | 2 |
| #23757650 | 2 |
| #23757474 | 2 |
| #23757473 | 2 |
| #23757016 | 2 |
| #23757005 | 2 |
| Q8⋊C8×C157 | 2 |
| #1620 | 157 |