Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
516 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23771990 | C2 | semidirect |
| 2. #23765136 | C2 | semidirect |
| 3. C2×#19098345 | C2 | semidirect |
| 4. #23761501 | C2 | semidirect |
| 16. #470×C79 | C4 | semidirect |
| 17. #469×C79 | C4 | semidirect |
| 34. #14579093 | D4 | semidirect |
| 39. C2×Q16×C79 | C2×C4 | semidirect |
| 41. C2×D8×C79 | C2×C4 | semidirect |
| 55. #106×C79 | C2×C4 | semidirect |
| 167. C79 | #13008 | semidirect |
| 173. #470 | Dic79 | semidirect |
| 174. #469 | Dic79 | semidirect |
| 187. C2×Q16 | C2×Dic79 | semidirect |
| 189. C2×D8 | C2×Dic79 | semidirect |
| 217. #106 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771990 | 2 |
| #23765136 | 2 |
| C2×#19098345 | 2 |
| #23761501 | 2 |
| C79×#3054 | 2 |
| #13008 | 79 |