Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
298 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 75 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. #23765629 | C2 | semidirect |
| 2. #23765450 | C2 | semidirect |
| 4. #23761458 | C2 | semidirect |
| 5. #23761364 | C2 | semidirect |
| 90. D4×C79 | Q32 | semidirect |
| 135. C79 | #12346 | semidirect |
| 220. D4 | #14579107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765629 | 2 |
| #23765450 | 2 |
| #23762765 | 2 |
| #23761458 | 2 |
| #23761364 | 2 |
| D4⋊(C79⋊C16) | 2 |
| C79×#3338 | 2 |
| #12346 | 79 |