Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
152 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 44. #11929441 | Q16 | semidirect |
| 71. C157 | #1591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758324 | 2 |
| #23758323 | 2 |
| #23758137 | 2 |
| #23758123 | 2 |
| Q8⋊#11929441 | 2 |
| C8×#11929441 | 2 |
| #23757365 | 2 |
| #1591 | 157 |