Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
414 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 59 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. #23764567 | C2 | semidirect |
| 2. #23762424 | C2 | semidirect |
| 4. #23761424 | C2 | semidirect |
| 6. #23761330 | C2 | semidirect |
| 204. C79 | #12267 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764567 | 2 |
| #23762424 | 2 |
| #23762322 | 2 |
| #23761424 | 2 |
| #23761397 | 2 |
| #23761330 | 2 |
| C79×#2752 | 2 |
| #12267 | 79 |