Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
384 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 384 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. #23775194 | C2 | semidirect |
| 2. #23765473 | C2 | semidirect |
| 3. #23763067 | C2 | semidirect |
| 4. #23761440 | C2 | semidirect |
| 5. #23761376 | C2 | semidirect |
| 6. #23761375 | C2 | semidirect |
| 7. C79×#2213 | C2 | semidirect |
| 19. #19098384 | C22 | semidirect |
| 21. #19098284 | C22 | semidirect |
| 23. #493×C79 | C22 | semidirect |
| 25. #364×C79 | C22 | semidirect |
| 83. Dic316 | D8 | semidirect |
| 95. D632 | D8 | semidirect |
| 108. Q16×C79 | D8 | semidirect |
| 114. D8×C79 | D8 | semidirect |
| 183. #2213 | D79 | semidirect |
| 188. C79 | #12314 | semidirect |
| 194. #493 | C2×D79 | semidirect |
| 204. #364 | C2×D79 | semidirect |
| 270. Q16 | #11929609 | semidirect |
| 289. D8 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775194 | 2 |
| #23765473 | 2 |
| #23763067 | 2 |
| #23761440 | 2 |
| #23761376 | 2 |
| #23761375 | 2 |
| C79×#2213 | 2 |
| #12314 | 79 |