Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23772977 | C2 | semidirect |
| 2. #23765136 | C2 | semidirect |
| 3. #23765010 | C2 | semidirect |
| 4. #23761502 | C2 | semidirect |
| 5. C79×#3414 | C2 | semidirect |
| 36. #14579093 | D4 | semidirect |
| 44. C2×Q16×C79 | D4 | semidirect |
| 46. C2×D8×C79 | D4 | semidirect |
| 52. C2×C16×C79 | D4 | semidirect |
| 143. #3414 | D79 | semidirect |
| 148. C79 | #13309 | semidirect |
| 170. C2×Q16 | C22⋊D79 | semidirect |
| 172. C2×D8 | C22⋊D79 | semidirect |
| 191. C2×C16 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772977 | 2 |
| #23765136 | 2 |
| #23765010 | 2 |
| #23761502 | 2 |
| C79×#3414 | 2 |
| #13309 | 79 |