Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
462 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19098376 | C2 | semidirect |
| 2. C2×#19098370 | C2 | semidirect |
| 3. #23765112 | C2 | semidirect |
| 4. C2×#19098364 | C2 | semidirect |
| 5. #23764185 | C2 | semidirect |
| 6. #23761489 | C2 | semidirect |
| 36. #14579097 | D4 | semidirect |
| 197. C79 | #13411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098376 | 2 |
| C2×#19098370 | 2 |
| #23765112 | 2 |
| C2×#19098364 | 2 |
| #23764185 | 2 |
| #23761489 | 2 |
| C79×#3155 | 2 |
| #13411 | 79 |