Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23765656 | C2 | semidirect |
| 2. #23765233 | C2 | semidirect |
| 3. #23762766 | C2 | semidirect |
| 5. #23761448 | C2 | semidirect |
| 6. #23761445 | C2 | semidirect |
| 7. C79×#1371 | C2 | semidirect |
| 73. C16×C79 | D8 | semidirect |
| 122. #1371 | D79 | semidirect |
| 125. C79 | #12435 | semidirect |
| 191. C16 | D632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765656 | 2 |
| #23765233 | 2 |
| #23762766 | 2 |
| #23762756 | 2 |
| #23761448 | 2 |
| #23761445 | 2 |
| C79×#1371 | 2 |
| #12435 | 79 |