Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23763133 | C2 | semidirect |
| 2. #23761714 | C2 | semidirect |
| 3. #23761400 | C2 | semidirect |
| 13. C2×C4×D4×C79 | C4 | semidirect |
| 15. #398×C79 | C4 | semidirect |
| 19. #394×C79 | C4 | semidirect |
| 21. C4×C4⋊C4×C79 | C4 | semidirect |
| 206. C79 | #11691 | semidirect |
| 208. C2×C4×D4 | Dic79 | semidirect |
| 212. #398 | Dic79 | semidirect |
| 216. #394 | Dic79 | semidirect |
| 218. C4×C4⋊C4 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763133 | 2 |
| #23761714 | 2 |
| #23761400 | 2 |
| #23761397 | 2 |
| C79×#2392 | 2 |
| #11691 | 79 |