Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
224 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 224 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 |
| 4. #23761464 | C2 | semidirect |
| 5. #23761380 | C2 | semidirect |
| 7. C8×C16×C79 | C2 | semidirect |
| 67. C16×C79 | SD16 | semidirect |
| 84. C8×C79 | M32 | semidirect |
| 112. C8×C16 | D79 | semidirect |
| 113. C79 | #12051 | semidirect |
| 173. C16 | #11929613 | semidirect |
| 192. C8 | #14579100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765308 | 2 |
| #23765233 | 2 |
| C8×#11929613 | 2 |
| #23761464 | 2 |
| #23761380 | 2 |
| #23761356 | 2 |
| C8×C16×C79 | 2 |
| #12051 | 79 |