Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
370 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 370 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. #23758002 | C2 | semidirect |
| 3. #23757624 | C2 | semidirect |
| 4. #23757559 | C2 | semidirect |
| 7. C8×Q8×C157 | C2 | semidirect |
| 53. Q8×C157 | SD16 | semidirect |
| 74. C157 | #3359 | semidirect |
| 81. C8×Q8 | D157 | semidirect |
| 122. Q8 | #14578943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758002 | 2 |
| Q8×D628 | 2 |
| #23757624 | 2 |
| #23757559 | 2 |
| #23757479 | 2 |
| C4×#14578943 | 2 |
| C8×Q8×C157 | 2 |
| #3359 | 157 |