Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
664 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 151 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. C2×Q32×D79 | C2 | semidirect |
| 3. #23765488 | C2 | semidirect |
| 4. #23765447 | C2 | semidirect |
| 5. #23765332 | C2 | semidirect |
| 6. C4×Dic632 | C2 | semidirect |
| 8. C79×#2247 | C2 | semidirect |
| 41. Dic632 | D4 | semidirect |
| 100. D316 | Q32 | semidirect |
| 114. C2×D79 | C2×Q32 | semidirect |
| 117. C4×C79 | C2×Q32 | semidirect |
| 130. #2247 | D79 | semidirect |
| 136. C79 | D4×Q32 | semidirect |
| 248. C4 | Q32×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D79 | 2 |
| #23775150 | 2 |
| #23765488 | 2 |
| #23765447 | 2 |
| #23765332 | 2 |
| C4×Dic632 | 2 |
| C16×D316 | 2 |
| C79×#2247 | 2 |
| D4×Q32 | 79 |