Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
654 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23774399 | C2 | semidirect |
| 3. #23764345 | C2 | semidirect |
| 4. #23761999 | C2 | semidirect |
| 5. #23761843 | C2 | semidirect |
| 6. #23761255 | C2 | semidirect |
| 7. C79×#3110 | C2 | semidirect |
| 52. C4⋊(C79⋊C8) | D4 | semidirect |
| 63. C4⋊Q8×C79 | D4 | semidirect |
| 64. C4⋊Q8×C79 | D4 | semidirect |
| 83. #97×C79 | D4 | semidirect |
| 229. #3110 | D79 | semidirect |
| 235. C79 | #10008 | semidirect |
| 270. C4⋊Q8 | C22⋊D79 | semidirect |
| 271. C4⋊Q8 | C22⋊D79 | 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 |
|---|---|
| #23774399 | 2 |
| #23768339 | 2 |
| #23764345 | 2 |
| #23761999 | 2 |
| #23761843 | 2 |
| #23761255 | 2 |
| C79×#3110 | 2 |
| #10008 | 79 |