Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 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×#19099006 | C2 | semidirect |
| 3. C2×#19098821 | C2 | semidirect |
| 4. C2×#19098374 | C2 | semidirect |
| 5. #23765121 | C2 | semidirect |
| 6. #23761506 | C2 | semidirect |
| 7. C2×#349×C79 | C2 | semidirect |
| 43. C2×Dic316 | D4 | semidirect |
| 62. #14579093 | D4 | semidirect |
| 78. M32×C79 | D4 | semidirect |
| 217. C2×#349 | D79 | semidirect |
| 219. C79 | #13317 | semidirect |
| 283. M32 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099006 | 2 |
| #23773009 | 2 |
| C2×#19098821 | 2 |
| C2×#19098374 | 2 |
| #23765121 | 2 |
| #23761506 | 2 |
| C2×#349×C79 | 2 |
| #13317 | 79 |