Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
394 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C2×#19098386 | C2 | semidirect |
| 4. #23764191 | C2 | semidirect |
| 5. #23761500 | C2 | semidirect |
| 6. #23761485 | C2 | semidirect |
| 25. #359×C79 | C4 | semidirect |
| 59. C2×C16×C79 | C2×C4 | semidirect |
| 61. #108×C79 | C2×C4 | semidirect |
| 159. C79 | #12949 | semidirect |
| 176. #359 | Dic79 | semidirect |
| 202. C2×C16 | C2×Dic79 | semidirect |
| 207. #108 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772284 | 2 |
| C2×#19098386 | 2 |
| #23765149 | 2 |
| #23764191 | 2 |
| #23761500 | 2 |
| #23761485 | 2 |
| C79×#2143 | 2 |
| #12949 | 79 |