Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
686 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 686 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. #23773396 | C2 | semidirect |
| 2. #23768297 | C2 | semidirect |
| 3. #23761960 | C2 | semidirect |
| 4. #23761824 | C2 | semidirect |
| 5. #23761791 | C2 | semidirect |
| 6. #23761260 | C2 | semidirect |
| 7. C79×#3036 | C2 | semidirect |
| 56. C4×C79⋊C8 | D4 | semidirect |
| 68. C4⋊Q8×C79 | D4 | semidirect |
| 69. #127×C79 | D4 | semidirect |
| 83. C4⋊C8×C79 | D4 | semidirect |
| 127. C2×D4×C79 | D8 | semidirect |
| 258. #3036 | D79 | semidirect |
| 264. C79 | #9996 | semidirect |
| 302. C4⋊Q8 | C22⋊D79 | semidirect |
| 303. #127 | C22⋊D79 | semidirect |
| 331. C4⋊C8 | C22⋊D79 | semidirect |
| 365. C2×D4 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773396 | 2 |
| #23768297 | 2 |
| #23761960 | 2 |
| #23761824 | 2 |
| #23761791 | 2 |
| #23761260 | 2 |
| C79×#3036 | 2 |
| #9996 | 79 |