Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1216 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 1216 conjugacy classes of subgroups — too many to draw. Only its 135 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. #23765069 | C2 | semidirect |
| 2. #23763315 | C2 | semidirect |
| 5. C2×#14579076 | C22 | semidirect |
| 9. C2×H(5,𝔽2)×C79 | C4 | semidirect |
| 15. #525×C79 | C4 | semidirect |
| 17. #518×C79 | C4 | semidirect |
| 66. C2×Q8×C79 | C22⋊C4 | semidirect |
| 82. C2×D4×C79 | C22⋊C4 | semidirect |
| 98. C42×C79 | C22⋊C4 | semidirect |
| 178. C79 | #12707 | semidirect |
| 179. C2×H(5,𝔽2) | Dic79 | semidirect |
| 185. #525 | Dic79 | semidirect |
| 187. #518 | Dic79 | semidirect |
| 237. C2×Q8 | C22⋊Dic79 | semidirect |
| 253. C2×D4 | C22⋊Dic79 | semidirect |
| 273. C42 | C22⋊Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765069 | 2 |
| #23763315 | 2 |
| C79×#3484 | 2 |
| #12707 | 79 |