Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
966 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 966 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23766220 | C2 | semidirect |
| 3. #23764235 | C2 | semidirect |
| 4. #23763330 | C2 | semidirect |
| 5. #23761967 | C2 | semidirect |
| 6. #23761247 | C2 | semidirect |
| 7. C79×#1289 | C2 | semidirect |
| 9. C22×D632 | C4 | semidirect |
| 16. C2×#14579083 | C4 | semidirect |
| 35. C22×D316 | C2×C4 | semidirect |
| 50. C2×C4⋊Dic79 | C2×C4 | semidirect |
| 69. C22×C8×C79 | C2×C4 | semidirect |
| 128. C22⋊Dic79 | D8 | semidirect |
| 227. D316 | #99 | semidirect |
| 294. #1289 | D79 | semidirect |
| 296. C79 | #9259 | semidirect |
| 335. C22×C8 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098699 | 2 |
| #23766220 | 2 |
| #23764235 | 2 |
| #23763330 | 2 |
| #23761967 | 2 |
| #23761247 | 2 |
| C79×#1289 | 2 |
| #9259 | 79 |