Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
294 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×Q32×D79 | C2 | semidirect |
| 2. C2×#19098402 | C2 | semidirect |
| 3. C2×#19098400 | C2 | semidirect |
| 5. #23761580 | C2 | semidirect |
| 6. (C2×D79)⋊C32 | C2 | semidirect |
| 7. C79×#1416 | C2 | semidirect |
| 32. Dic632 | D4 | semidirect |
| 43. Q32×C79 | D4 | semidirect |
| 99. C2×D79 | SD64 | semidirect |
| 117. #1416 | D79 | semidirect |
| 119. C79 | #13662 | semidirect |
| 148. Q32 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D79 | 2 |
| C2×#19098402 | 2 |
| C2×#19098400 | 2 |
| #23765487 | 2 |
| #23761580 | 2 |
| (C2×D79)⋊C32 | 2 |
| C79×#1416 | 2 |
| #13662 | 79 |