Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
432 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23763477 | C2 | semidirect |
| 2. #23761714 | C2 | semidirect |
| 3. #23761421 | C2 | semidirect |
| 12. C2×#124×C79 | C4 | semidirect |
| 14. #395×C79 | C4 | semidirect |
| 15. #394×C79 | C4 | semidirect |
| 22. #376×C79 | C4 | semidirect |
| 186. C79 | #11844 | semidirect |
| 187. C2×#124 | Dic79 | semidirect |
| 190. #395 | Dic79 | semidirect |
| 191. #394 | Dic79 | semidirect |
| 199. #376 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763477 | 2 |
| #23761714 | 2 |
| #23761421 | 2 |
| #23761397 | 2 |
| C79×#2610 | 2 |
| #11844 | 79 |