Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23757677 | C2 | semidirect |
| 3. #23757651 | C2 | semidirect |
| 4. #23757622 | C2 | semidirect |
| 8. C4×Dic628 | C2 | semidirect |
| 9. C4×#14578944 | C2 | semidirect |
| 11. C4×Q16×C157 | C2 | semidirect |
| 83. C4×D157 | Q16 | semidirect |
| 114. C157 | #3170 | semidirect |
| 125. C4×Q16 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757827 | 2 |
| #23757677 | 2 |
| #23757651 | 2 |
| #23757622 | 2 |
| #23757515 | 2 |
| #23757513 | 2 |
| #23757511 | 2 |
| C4×Dic628 | 2 |
| C4×#14578944 | 2 |
| C4×C8×D157 | 2 |
| C4×Q16×C157 | 2 |
| #3170 | 157 |