Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1034 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1034 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. #23765978 | C2 | semidirect |
| 2. #23763321 | C2 | semidirect |
| 3. #23761929 | C2 | semidirect |
| 4. #23761253 | C2 | semidirect |
| 14. C2×#127×C79 | C4 | semidirect |
| 19. #390×C79 | C4 | semidirect |
| 32. C79⋊#95 | D4 | semidirect |
| 42. C22×D4×C79 | C2×C4 | semidirect |
| 50. C2×C4⋊C4×C79 | C2×C4 | semidirect |
| 55. C2×C42×C79 | C2×C4 | semidirect |
| 226. C79 | #9463 | semidirect |
| 228. C2×#127 | Dic79 | semidirect |
| 236. #390 | Dic79 | semidirect |
| 251. C22×D4 | C2×Dic79 | semidirect |
| 261. C2×C4⋊C4 | C2×Dic79 | semidirect |
| 271. C2×C42 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765978 | 2 |
| #23763321 | 2 |
| #23761929 | 2 |
| #23761253 | 2 |
| C79×#2433 | 2 |
| #9463 | 79 |