Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
318 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 2. #23765614 | C2 | semidirect |
| 3. #23764974 | C2 | semidirect |
| 4. #23761386 | C2 | semidirect |
| 5. #23761385 | C2 | semidirect |
| 6. #23761350 | C2 | semidirect |
| 7. C79×#2238 | C2 | semidirect |
| 149. #2238 | D79 | semidirect |
| 154. C79 | #12307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774777 | 2 |
| #23765614 | 2 |
| #23764974 | 2 |
| #23761386 | 2 |
| #23761385 | 2 |
| #23761350 | 2 |
| C79×#2238 | 2 |
| #12307 | 79 |