Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
226 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 25. #14579107 | C8 | semidirect |
| 85. C79⋊C8 | Q32 | semidirect |
| 107. C79 | C8×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579107 | 2 |
| Q16×C79⋊C8 | 2 |
| #23762206 | 2 |
| #23761471 | 2 |
| #23761365 | 2 |
| C16×C79⋊C8 | 2 |
| C79×#1332 | 2 |
| C8×Q32 | 79 |