Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
382 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23757998 | C2 | semidirect |
| 3. #23757636 | C2 | semidirect |
| 4. #23757621 | C2 | semidirect |
| 5. #23757576 | C2 | semidirect |
| 6. #23757474 | C2 | semidirect |
| 7. #23757472 | C2 | semidirect |
| 8. #23757400 | C2 | semidirect |
| 9. #23757372 | C2 | semidirect |
| 10. C4×#14578942 | C2 | semidirect |
| 11. #474×C157 | C2 | semidirect |
| 77. Dic314 | #41 | semidirect |
| 124. C157 | #3368 | semidirect |
| 131. #474 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757998 | 2 |
| #23757944 | 2 |
| #23757636 | 2 |
| #23757621 | 2 |
| #23757576 | 2 |
| #23757474 | 2 |
| #23757472 | 2 |
| #23757400 | 2 |
| #23757372 | 2 |
| C4×#14578942 | 2 |
| #474×C157 | 2 |
| #3368 | 157 |