Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
252 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 252 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. C16×D316 | C2 | semidirect |
| 3. #23761464 | C2 | semidirect |
| 4. #23761356 | C2 | semidirect |
| 5. C79×#1312 | C2 | semidirect |
| 32. D632 | C16 | semidirect |
| 53. D316 | C2×C16 | semidirect |
| 59. C8×C79 | C2×C16 | semidirect |
| 81. #1312 | D79 | semidirect |
| 82. C79 | #12062 | semidirect |
| 137. C8 | C16×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D316 | 2 |
| C8×D632 | 2 |
| #23761464 | 2 |
| #23761356 | 2 |
| C79×#1312 | 2 |
| #12062 | 79 |