Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 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. #23757606 | C2 | semidirect |
| 3. #23757550 | C2 | semidirect |
| 4. #23757475 | C2 | semidirect |
| 6. #23757371 | C2 | semidirect |
| 7. #23757330 | C2 | semidirect |
| 8. #533×C157 | C2 | semidirect |
| 18. #19097704 | C22 | semidirect |
| 19. C4⋊#11929434 | C22 | semidirect |
| 20. #19097695 | C22 | semidirect |
| 23. #19097682 | C22 | semidirect |
| 24. C4⋊Q8×C157 | C22 | semidirect |
| 25. C4⋊Q8×C157 | C22 | semidirect |
| 30. C4×Q8×C157 | C22 | semidirect |
| 112. C157 | #3110 | semidirect |
| 114. #533 | D157 | semidirect |
| 125. C4⋊Q8 | C2×D157 | semidirect |
| 126. C4⋊Q8 | C2×D157 | semidirect |
| 131. C4×Q8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D628 | 2 |
| #23757606 | 2 |
| #23757550 | 2 |
| #23757475 | 2 |
| #23757423 | 2 |
| #23757371 | 2 |
| #23757330 | 2 |
| #533×C157 | 2 |
| #3110 | 157 |