Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
458 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 71 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. D8×D316 | C2 | semidirect |
| 2. #23765650 | C2 | semidirect |
| 3. #23765435 | C2 | semidirect |
| 4. #23762756 | C2 | semidirect |
| 5. #23761445 | C2 | semidirect |
| 6. #23761356 | C2 | semidirect |
| 7. C79×#1331 | C2 | semidirect |
| 13. #19098940 | C22 | semidirect |
| 19. C4⋊(C79⋊C16) | C22 | semidirect |
| 23. C4×C16×C79 | C22 | semidirect |
| 24. #335×C79 | C22 | semidirect |
| 89. D8×C79 | D8 | semidirect |
| 126. D316 | D16 | semidirect |
| 168. #1331 | D79 | semidirect |
| 170. C79 | #12316 | semidirect |
| 185. C4×C16 | C2×D79 | semidirect |
| 186. #335 | C2×D79 | semidirect |
| 245. D8 | D632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D316 | 2 |
| #23765650 | 2 |
| #23765435 | 2 |
| #23762756 | 2 |
| #23761445 | 2 |
| #23761356 | 2 |
| C79×#1331 | 2 |
| #12316 | 79 |