Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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. #41×Dic157 | C2 | semidirect |
| 2. #23757385 | C2 | semidirect |
| 3. #23757380 | C2 | semidirect |
| 4. #23757374 | C2 | semidirect |
| 5. #23757311 | C2 | semidirect |
| 6. #23757269 | C2 | semidirect |
| 7. C2×#19097681 | C2 | semidirect |
| 24. #135×C157 | C4 | semidirect |
| 42. #41×C157 | C2×C4 | semidirect |
| 48. Q16×C157 | C2×C4 | semidirect |
| 49. SD16×C157 | C2×C4 | semidirect |
| 50. D8×C157 | C2×C4 | semidirect |
| 51. C2×C8×C157 | C2×C4 | semidirect |
| 89. C157 | #2943 | semidirect |
| 100. #135 | Dic157 | semidirect |
| 120. #41 | C2×Dic157 | semidirect |
| 128. Q16 | C2×Dic157 | semidirect |
| 129. SD16 | C2×Dic157 | semidirect |
| 130. D8 | C2×Dic157 | semidirect |
| 133. C2×C8 | C2×Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic157 | 2 |
| #23757385 | 2 |
| #23757380 | 2 |
| #23757374 | 2 |
| #23757311 | 2 |
| #23757269 | 2 |
| C2×#19097681 | 2 |
| C2×#135×C157 | 2 |
| #2943 | 157 |