Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
662 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 127 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. C22×#14579104 | C2 | semidirect |
| 3. C2×#19098363 | C2 | semidirect |
| 4. #23761478 | C2 | semidirect |
| 5. C79×#1969 | C2 | semidirect |
| 36. C2×C79⋊C16 | D4 | semidirect |
| 41. C2×Q16×C79 | D4 | semidirect |
| 106. C2×C4×C79 | SD32 | semidirect |
| 148. #1969 | D79 | semidirect |
| 150. C79 | #13328 | semidirect |
| 171. C2×Q16 | D316 | semidirect |
| 256. C2×C4 | #14579104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579104 | 2 |
| C2×#19098940 | 2 |
| C2×#19098363 | 2 |
| #23761478 | 2 |
| C79×#1969 | 2 |
| #13328 | 79 |