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 |
| 7. Q16×Dic157 | C2 | semidirect |
| 8. #23757367 | C2 | semidirect |
| 9. #23757365 | C2 | semidirect |
| 77. C2×Dic157 | Q16 | semidirect |
| 114. C157 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757825 | 2 |
| #23757677 | 2 |
| #23757651 | 2 |
| #23757622 | 2 |
| #23757514 | 2 |
| #23757512 | 2 |
| Q16×Dic157 | 2 |
| #23757367 | 2 |
| #23757365 | 2 |
| C2×C8×Dic157 | 2 |
| #467×C157 | 2 |
| #3170 | 157 |