Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
210 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 82. C8×C79 | Q32 | semidirect |
| 107. C79 | #12072 | semidirect |
| 183. C8 | #14579107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579107 | 2 |
| C8×Dic316 | 2 |
| #23761471 | 2 |
| #23761364 | 2 |
| #23761363 | 2 |
| #23761318 | 2 |
| C79×#1591 | 2 |
| #12072 | 79 |