Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#19097790 | C2 | semidirect |
| 2. #23757943 | C2 | semidirect |
| 3. #23757927 | C2 | semidirect |
| 4. #23757645 | C2 | semidirect |
| 5. #23757501 | C2 | semidirect |
| 6. #23757484 | C2 | semidirect |
| 7. #23757436 | C2 | semidirect |
| 8. #23757415 | C2 | semidirect |
| 9. C4×#14578942 | C2 | semidirect |
| 10. #23757338 | C2 | semidirect |
| 11. #459×C157 | C2 | semidirect |
| 58. #14578942 | D4 | semidirect |
| 127. C4×C157 | #135 | semidirect |
| 140. C157 | #3284 | semidirect |
| 148. #459 | D157 | semidirect |
| 272. C4 | #19097790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097790 | 2 |
| #23757943 | 2 |
| #23757927 | 2 |
| #23757645 | 2 |
| #23757501 | 2 |
| #23757484 | 2 |
| #23757436 | 2 |
| #23757415 | 2 |
| C4×#14578942 | 2 |
| #23757338 | 2 |
| #459×C157 | 2 |
| #3284 | 157 |