Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
508 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23768406 | C2 | semidirect |
| 4. #23761278 | C2 | semidirect |
| 5. #23761267 | C2 | semidirect |
| 6. #23761248 | C2 | semidirect |
| 52. C22×D4×C79 | Q8 | semidirect |
| 59. C2×C4⋊C4×C79 | Q8 | semidirect |
| 237. C79 | #10374 | semidirect |
| 259. C22×D4 | Dic158 | semidirect |
| 277. C2×C4⋊C4 | Dic158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23768406 | 2 |
| #23761968 | 2 |
| C2×#19098297 | 2 |
| #23761278 | 2 |
| #23761267 | 2 |
| #23761248 | 2 |
| C79×#1964 | 2 |
| #10374 | 79 |