Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19098998 | C2 | semidirect |
| 2. #23773116 | C2 | semidirect |
| 3. #23773049 | C2 | semidirect |
| 4. C2×#19098377 | C2 | semidirect |
| 5. #23765027 | C2 | semidirect |
| 6. #23761516 | C2 | semidirect |
| 7. C79×#2145 | C2 | semidirect |
| 59. #14579101 | D4 | semidirect |
| 62. #14579097 | D4 | semidirect |
| 71. C2×Q16×C79 | D4 | semidirect |
| 73. C2×D8×C79 | D4 | semidirect |
| 216. #2145 | D79 | semidirect |
| 219. C79 | #13310 | semidirect |
| 255. C2×Q16 | D316 | semidirect |
| 263. C2×D8 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098998 | 2 |
| #23773116 | 2 |
| #23773049 | 2 |
| C2×#19098377 | 2 |
| #23765027 | 2 |
| #23761516 | 2 |
| C79×#2145 | 2 |
| #13310 | 79 |