Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
226 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23765308 | C2 | semidirect |
| 3. #23761463 | C2 | semidirect |
| 4. #23761378 | C2 | semidirect |
| 6. #23761316 | C2 | semidirect |
| 67. C16×C79 | SD16 | semidirect |
| 113. C79 | #12049 | semidirect |
| 173. C16 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765308 | 2 |
| C8×#11929612 | 2 |
| #23761463 | 2 |
| #23761378 | 2 |
| D4⋊(C79⋊C16) | 2 |
| #23761316 | 2 |
| D4×C16×C79 | 2 |
| #12049 | 79 |