Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
572 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 572 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. C2×#19098830 | C2 | semidirect |
| 2. #23773044 | C2 | semidirect |
| 3. C2×#19098376 | C2 | semidirect |
| 4. #23765116 | C2 | semidirect |
| 5. C2×#19098346 | C2 | semidirect |
| 6. #23761496 | C2 | semidirect |
| 7. C22×D16×C79 | C2 | semidirect |
| 51. #14579097 | D4 | semidirect |
| 69. C2×D8×C79 | D4 | semidirect |
| 74. C2×C16×C79 | D4 | semidirect |
| 200. C22×D16 | D79 | semidirect |
| 207. C79 | #13319 | semidirect |
| 247. C2×D8 | C22⋊D79 | semidirect |
| 268. C2×C16 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098830 | 2 |
| #23773044 | 2 |
| C2×#19098376 | 2 |
| #23765116 | 2 |
| C2×#19098346 | 2 |
| #23761496 | 2 |
| C22×D16×C79 | 2 |
| #13319 | 79 |