Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 424 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. C2×#19097770 | C2 | semidirect |
| 3. #23757634 | C2 | semidirect |
| 4. #23757631 | C2 | semidirect |
| 5. #23757622 | C2 | semidirect |
| 6. #23757618 | C2 | semidirect |
| 7. #23757275 | C2 | semidirect |
| 8. #23757274 | C2 | semidirect |
| 9. #23757272 | C2 | semidirect |
| 10. M16×Dic157 | C2 | semidirect |
| 11. #417×C157 | C2 | semidirect |
| 149. C157 | #3141 | semidirect |
| 160. #417 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757819 | 2 |
| C2×#19097770 | 2 |
| #23757634 | 2 |
| #23757631 | 2 |
| #23757622 | 2 |
| #23757618 | 2 |
| #23757275 | 2 |
| #23757274 | 2 |
| #23757272 | 2 |
| M16×Dic157 | 2 |
| #417×C157 | 2 |
| #3141 | 157 |