Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
286 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23761594 | C2 | semidirect |
| 5. #23761593 | C2 | semidirect |
| 6. #23761592 | C2 | semidirect |
| 7. C79×#1420 | C2 | semidirect |
| 118. D79 | #1420 | direct (N × H) |
| 125. #1420 | D79 | direct (N × H) |
| 126. C79 | C2×#1420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D79 | 2 |
| M64×D79 | 2 |
| #368×D79 | 2 |
| #23761594 | 2 |
| #23761593 | 2 |
| #23761592 | 2 |
| C79×#1420 | 2 |
| C2×#1420 | 79 |