Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#19099004 | C2 | semidirect |
| 3. C2×#19098818 | C2 | semidirect |
| 4. C2×#19098374 | C2 | semidirect |
| 5. C2×#19098344 | C2 | semidirect |
| 6. #23761505 | C2 | semidirect |
| 7. C79×#2141 | C2 | semidirect |
| 60. #14579101 | D4 | semidirect |
| 63. #14579093 | D4 | semidirect |
| 73. C2×Q16×C79 | D4 | semidirect |
| 216. #2141 | D79 | semidirect |
| 219. C79 | #13317 | semidirect |
| 256. C2×Q16 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099004 | 2 |
| #23773010 | 2 |
| C2×#19098818 | 2 |
| C2×#19098374 | 2 |
| C2×#19098344 | 2 |
| #23761505 | 2 |
| C79×#2141 | 2 |
| #13317 | 79 |