Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
534 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. #23764217 | C2 | semidirect |
| 3. #23764216 | C2 | semidirect |
| 4. #23763568 | C2 | semidirect |
| 5. C2×#19098302 | C2 | semidirect |
| 6. #23761282 | C2 | semidirect |
| 7. C2×#329×C79 | C2 | semidirect |
| 75. #97×C79 | D4 | semidirect |
| 243. C2×#329 | D79 | semidirect |
| 245. C79 | #10424 | semidirect |
| 309. #97 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771445 | 2 |
| #23764217 | 2 |
| #23764216 | 2 |
| #23763568 | 2 |
| C2×#19098302 | 2 |
| #23761282 | 2 |
| C2×#329×C79 | 2 |
| #10424 | 79 |