Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
662 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 119 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. C22×#14579105 | C2 | semidirect |
| 4. C2×#19098363 | C2 | semidirect |
| 5. #23764259 | C2 | semidirect |
| 6. #23761477 | C2 | semidirect |
| 7. C2×#357×C79 | C2 | semidirect |
| 37. C2×Dic316 | D4 | semidirect |
| 55. C2×C79⋊C16 | D4 | semidirect |
| 71. C2×C16×C79 | D4 | semidirect |
| 158. C2×Dic79 | SD32 | semidirect |
| 206. C2×#357 | D79 | semidirect |
| 209. C79 | #13328 | semidirect |
| 269. C2×C16 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579106 | 2 |
| C22×#14579105 | 2 |
| C2×#19098938 | 2 |
| C2×#19098363 | 2 |
| #23764259 | 2 |
| #23761477 | 2 |
| C2×#357×C79 | 2 |
| #13328 | 79 |