Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
978 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 978 conjugacy classes of subgroups — too many to draw. Only its 191 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 |
|---|---|---|
| 2. #23774348 | C2 | semidirect |
| 3. #23762356 | C2 | semidirect |
| 4. #23761898 | C2 | semidirect |
| 96. C2×D4×C79 | Q16 | semidirect |
| 181. C79 | #18390 | semidirect |
| 256. C2×D4 | #11929614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777203 | 2 |
| #23774348 | 2 |
| #23762356 | 2 |
| #23761898 | 2 |
| #23761721 | 2 |
| C79×#2563 | 2 |
| #18390 | 79 |