Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
454 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23765149 | C2 | semidirect |
| 2. C2×#19098376 | C2 | semidirect |
| 3. C2×#19098376 | C2 | semidirect |
| 4. #23765128 | C2 | semidirect |
| 5. #23764190 | C2 | semidirect |
| 6. #23761486 | C2 | semidirect |
| 38. #14579097 | D4 | semidirect |
| 182. C79 | #13417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765149 | 2 |
| C2×#19098376 | 2 |
| #23765128 | 2 |
| #23764190 | 2 |
| #23761486 | 2 |
| C79×#3155 | 2 |
| #13417 | 79 |