Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#19097769 | C2 | semidirect |
| 4. #23757476 | C2 | direct (N × H) |
| 5. C2×#19097700 | C2 | semidirect |
| 6. C2×#19097696 | C2 | semidirect |
| 7. C2×#19097695 | C2 | semidirect |
| 15. #19097769 | C22 | semidirect |
| 23. #19097700 | C22 | semidirect |
| 24. #19097696 | C22 | semidirect |
| 25. #19097695 | C22 | semidirect |
| 74. C2×Dic157 | SD16 | semidirect |
| 111. Dic157 | C2×SD16 | semidirect |
| 113. C2×C157 | #461 | semidirect |
| 117. C157 | C2×#461 | semidirect |
| 231. C2 | #23757476 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578942 | 2 |
| C2×#19097769 | 2 |
| C2×D4×Dic157 | 2 |
| #23757476 | 2 |
| C2×#19097700 | 2 |
| C2×#19097696 | 2 |
| C2×#19097695 | 2 |
| C22×SD16×C157 | 2 |
| C2×#461 | 157 |