Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
576 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23766512 | C2 | semidirect |
| 2. #23762024 | C2 | semidirect |
| 3. #23761908 | C2 | semidirect |
| 4. #23761294 | C2 | semidirect |
| 19. #497×C79 | C4 | semidirect |
| 20. #496×C79 | C4 | semidirect |
| 48. C4⋊Q8×C79 | C2×C4 | semidirect |
| 49. #127×C79 | C2×C4 | semidirect |
| 58. #97×C79 | C2×C4 | semidirect |
| 176. C79 | #9441 | semidirect |
| 181. #497 | Dic79 | semidirect |
| 182. #496 | Dic79 | semidirect |
| 207. C4⋊Q8 | C2×Dic79 | semidirect |
| 208. #127 | C2×Dic79 | semidirect |
| 225. #97 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766512 | 2 |
| #23762024 | 2 |
| #23761908 | 2 |
| #23761294 | 2 |
| C79×#3153 | 2 |
| #9441 | 79 |