Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
406 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 406 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. #23775200 | C2 | semidirect |
| 2. #23765473 | C2 | semidirect |
| 3. #23763014 | C2 | semidirect |
| 4. #23761436 | C2 | semidirect |
| 5. #23761373 | C2 | semidirect |
| 6. #23761372 | C2 | semidirect |
| 7. C79×#2213 | C2 | semidirect |
| 17. #19098384 | C22 | semidirect |
| 19. C8×C79⋊C8 | C22 | semidirect |
| 21. #493×C79 | C22 | semidirect |
| 23. #364×C79 | C22 | semidirect |
| 66. Dic316 | D8 | semidirect |
| 75. D632 | D8 | semidirect |
| 86. Q16×C79 | D8 | semidirect |
| 92. D8×C79 | D8 | semidirect |
| 151. #2213 | D79 | semidirect |
| 156. C79 | #12310 | semidirect |
| 163. #493 | C2×D79 | semidirect |
| 170. #364 | C2×D79 | semidirect |
| 219. Q16 | #11929609 | semidirect |
| 236. D8 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775200 | 2 |
| #23765473 | 2 |
| #23763014 | 2 |
| #23761436 | 2 |
| #23761373 | 2 |
| #23761372 | 2 |
| C79×#2213 | 2 |
| #12310 | 79 |