Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
496 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #23765120 | C2 | semidirect |
| 4. #23764316 | C2 | semidirect |
| 5. #23761496 | C2 | semidirect |
| 6. #23761488 | C2 | semidirect |
| 24. C2×SD32×C79 | C4 | semidirect |
| 52. C2×Q16×C79 | C2×C4 | semidirect |
| 63. C2×C16×C79 | C2×C4 | semidirect |
| 168. C79 | #13019 | semidirect |
| 174. C2×SD32 | Dic79 | semidirect |
| 194. C2×Q16 | C2×Dic79 | semidirect |
| 215. C2×C16 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772252 | 2 |
| C2×#19098376 | 2 |
| #23765120 | 2 |
| #23764316 | 2 |
| #23761496 | 2 |
| #23761488 | 2 |
| C22×SD32×C79 | 2 |
| #13019 | 79 |