Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23773923 | C2 | semidirect |
| 4. #23761516 | C2 | semidirect |
| 5. #23761515 | C2 | semidirect |
| 6. #23761479 | C2 | semidirect |
| 49. C2×Q16×C79 | Q8 | semidirect |
| 51. C2×D8×C79 | Q8 | semidirect |
| 156. C79 | #13373 | semidirect |
| 177. C2×Q16 | Dic158 | semidirect |
| 179. C2×D8 | Dic158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773923 | 2 |
| #23765136 | 2 |
| #23764294 | 2 |
| #23761516 | 2 |
| #23761515 | 2 |
| #23761479 | 2 |
| C79×#2145 | 2 |
| #13373 | 79 |