Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
416 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23764624 | C2 | semidirect |
| 2. #23762402 | C2 | semidirect |
| 4. #23761406 | C2 | semidirect |
| 5. #23761403 | C2 | semidirect |
| 6. #23761346 | C2 | semidirect |
| 7. C79×#2823 | C2 | semidirect |
| 114. C42×C79 | D8 | semidirect |
| 196. #2823 | D79 | semidirect |
| 203. C79 | #12155 | semidirect |
| 310. C42 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764624 | 2 |
| #23762402 | 2 |
| #23762334 | 2 |
| #23761406 | 2 |
| #23761403 | 2 |
| #23761346 | 2 |
| C79×#2823 | 2 |
| #12155 | 79 |