Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
604 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#19098816 | C2 | semidirect |
| 3. C2×#19098373 | C2 | semidirect |
| 4. #23765115 | C2 | semidirect |
| 5. C2×#19098345 | C2 | semidirect |
| 6. #23761505 | C2 | semidirect |
| 7. C79×#3054 | C2 | semidirect |
| 38. C2×D632 | D4 | semidirect |
| 48. #14579101 | D4 | semidirect |
| 52. #14579093 | D4 | semidirect |
| 60. C2×Q16×C79 | D4 | semidirect |
| 62. C2×D8×C79 | D4 | semidirect |
| 77. #107×C79 | D4 | semidirect |
| 222. #3054 | D79 | semidirect |
| 228. C79 | #13316 | semidirect |
| 260. C2×Q16 | C22⋊D79 | semidirect |
| 268. C2×D8 | C22⋊D79 | semidirect |
| 295. #107 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098998 | 2 |
| C2×#19098816 | 2 |
| C2×#19098373 | 2 |
| #23765115 | 2 |
| C2×#19098345 | 2 |
| #23761505 | 2 |
| C79×#3054 | 2 |
| #13316 | 79 |