Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
194 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23765286 | C2 | semidirect |
| 2. #23765276 | C2 | semidirect |
| 3. #23761606 | C2 | semidirect |
| 4. #23761590 | C2 | semidirect |
| 5. #23761587 | C2 | semidirect |
| 6. #23761535 | C2 | semidirect |
| 18. SD64×C79 | C4 | semidirect |
| 19. D32×C79 | C4 | semidirect |
| 32. Q32×C79 | C2×C4 | semidirect |
| 36. D16×C79 | C2×C4 | semidirect |
| 38. C32×C79 | C2×C4 | semidirect |
| 95. C79 | #13658 | semidirect |
| 100. SD64 | Dic79 | semidirect |
| 101. D32 | Dic79 | semidirect |
| 113. Q32 | C2×Dic79 | semidirect |
| 117. D16 | C2×Dic79 | semidirect |
| 126. C32 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765286 | 2 |
| #23765276 | 2 |
| #23761606 | 2 |
| #23761590 | 2 |
| #23761587 | 2 |
| #23761535 | 2 |
| C79×#2263 | 2 |
| #13658 | 79 |