Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
632 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 632 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. #23773409 | C2 | semidirect |
| 2. #23773197 | C2 | semidirect |
| 4. #23761965 | C2 | semidirect |
| 5. #23761826 | C2 | semidirect |
| 6. #23761259 | C2 | semidirect |
| 7. C79×#1478 | C2 | semidirect |
| 38. #14579161 | D4 | semidirect |
| 39. #14579161 | D4 | semidirect |
| 61. C4⋊(C79⋊C8) | D4 | semidirect |
| 83. C4×C8×C79 | D4 | semidirect |
| 127. C2×D4×C79 | SD16 | semidirect |
| 243. #1478 | D79 | semidirect |
| 245. C79 | #10000 | semidirect |
| 318. C4×C8 | C22⋊D79 | semidirect |
| 337. C2×D4 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773409 | 2 |
| #23773197 | 2 |
| #23768297 | 2 |
| #23761965 | 2 |
| #23761826 | 2 |
| #23761259 | 2 |
| C79×#1478 | 2 |
| #10000 | 79 |