Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic314 | C2 | semidirect |
| 3. #23757624 | C2 | semidirect |
| 4. #23757604 | C2 | semidirect |
| 5. #23757559 | C2 | semidirect |
| 6. #23757502 | C2 | semidirect |
| 7. #23757479 | C2 | semidirect |
| 8. #23757414 | C2 | semidirect |
| 9. C4×#14578943 | C2 | semidirect |
| 10. C2×#19097696 | C2 | semidirect |
| 11. C8×D4×C157 | C2 | semidirect |
| 83. Dic314 | #41 | semidirect |
| 96. D4×C157 | SD16 | semidirect |
| 128. C157 | #3298 | semidirect |
| 139. C8×D4 | D157 | semidirect |
| 217. D4 | #14578943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic314 | 2 |
| #23757927 | 2 |
| #23757624 | 2 |
| #23757604 | 2 |
| #23757559 | 2 |
| #23757502 | 2 |
| #23757479 | 2 |
| #23757414 | 2 |
| C4×#14578943 | 2 |
| C2×#19097696 | 2 |
| C8×D4×C157 | 2 |
| #3298 | 157 |