Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23765682 | C2 | semidirect |
| 2. #23765627 | C2 | semidirect |
| 4. #23762994 | C2 | semidirect |
| 6. C16×C79⋊C8 | C2 | semidirect |
| 68. C16×C79 | SD16 | semidirect |
| 87. C79⋊C8 | SD32 | semidirect |
| 111. C79 | #12505 | semidirect |
| 172. C16 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765682 | 2 |
| #23765627 | 2 |
| #23765623 | 2 |
| #23762994 | 2 |
| #23762989 | 2 |
| C16×C79⋊C8 | 2 |
| C79×#2248 | 2 |
| #12505 | 79 |