Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23758039 | C2 | semidirect |
| 3. #23757278 | C2 | semidirect |
| 4. #23757246 | C2 | semidirect |
| 5. #23757030 | C2 | semidirect |
| 6. #23757029 | C2 | semidirect |
| 7. #418×C157 | C2 | semidirect |
| 13. #19097767 | C4 | semidirect |
| 14. #19097758 | C4 | semidirect |
| 37. C2×#11929434 | D4 | semidirect |
| 56. C2×C8×C157 | D4 | semidirect |
| 115. C157 | #1910 | semidirect |
| 120. #418 | D157 | semidirect |
| 165. C2×C8 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758039 | 2 |
| #23757840 | 2 |
| #23757278 | 2 |
| #23757246 | 2 |
| #23757030 | 2 |
| #23757029 | 2 |
| #418×C157 | 2 |
| #1910 | 157 |