Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
302 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #23761582 | C2 | semidirect |
| 5. #23761581 | C2 | semidirect |
| 6. #23761580 | C2 | semidirect |
| 7. C79×#1416 | C2 | semidirect |
| 12. Q32×D79 | C4 | semidirect |
| 30. Dic632 | C2×C4 | semidirect |
| 40. Q32×C79 | C2×C4 | semidirect |
| 101. D79 | #1416 | direct (N × H) |
| 108. #1416 | D79 | direct (N × H) |
| 109. C79 | C2×#1416 | semidirect |
| 136. Q32 | C4×D79 | 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×C32×D79 | 2 |
| #366×D79 | 2 |
| #23761582 | 2 |
| #23761581 | 2 |
| #23761580 | 2 |
| C79×#1416 | 2 |
| C2×#1416 | 79 |