Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
242 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 101 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. #23765232 | C2 | semidirect |
| 2. D4×C79⋊C16 | C2 | semidirect |
| 3. #23761464 | C2 | semidirect |
| 4. D4⋊(C79⋊C16) | C2 | semidirect |
| 5. D4⋊(C79⋊C16) | C2 | semidirect |
| 6. #23761318 | C2 | semidirect |
| 76. D4×C79 | M32 | semidirect |
| 121. C79 | #12063 | semidirect |
| 190. D4 | #14579101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765232 | 2 |
| D4×C79⋊C16 | 2 |
| #23761464 | 2 |
| D4⋊(C79⋊C16) | 2 |
| #23761318 | 2 |
| C8×D8×C79 | 2 |
| #12063 | 79 |