Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
242 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 242 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 |
|---|---|---|
| 2. C8×Dic316 | C2 | semidirect |
| 4. #23761474 | C2 | semidirect |
| 5. #23761365 | C2 | semidirect |
| 7. C8×C16×C79 | C2 | semidirect |
| 28. #14579106 | C8 | direct (N × H) |
| 48. Dic316 | C2×C8 | semidirect |
| 67. C16×C79 | C2×C8 | semidirect |
| 84. C8×C79 | SD32 | semidirect |
| 112. C8×C16 | D79 | semidirect |
| 113. C79 | C8×SD32 | semidirect |
| 173. C16 | C8×D79 | semidirect |
| 192. C8 | #14579106 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579106 | 2 |
| C8×Dic316 | 2 |
| C8×D632 | 2 |
| #23761474 | 2 |
| #23761365 | 2 |
| #23761362 | 2 |
| C8×C16×C79 | 2 |
| C8×SD32 | 79 |