Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
918 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 267 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. C22×#14579106 | C2 | semidirect |
| 2. C2×#19098943 | C2 | semidirect |
| 4. #23765656 | C2 | direct (N × H) |
| 5. C2×C4×C16×C79 | C2 | semidirect |
| 13. C2×#14579106 | C22 | semidirect |
| 15. #19098943 | C22 | semidirect |
| 20. C4×C16×C79 | C22 | semidirect |
| 43. C2×C16×C79 | D4 | semidirect |
| 75. C16×C79 | C2×D4 | semidirect |
| 80. C2×C4×C79 | SD32 | semidirect |
| 105. C4×C79 | C2×SD32 | semidirect |
| 110. C2×C79 | #2248 | semidirect |
| 118. C2×C4×C16 | D79 | semidirect |
| 119. C79 | C2×#2248 | semidirect |
| 134. C4×C16 | C2×D79 | semidirect |
| 157. C2×C16 | D316 | semidirect |
| 189. C16 | C2×D316 | semidirect |
| 203. C2×C4 | #14579106 | semidirect |
| 220. C4 | C2×#14579106 | semidirect |
| 224. C2 | #23765656 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579106 | 2 |
| C2×#19098943 | 2 |
| C2×#19098940 | 2 |
| #23765656 | 2 |
| C2×C4×C16×C79 | 2 |
| C2×#2248 | 79 |