Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
238 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 99 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. C16×Dic158 | C2 | semidirect |
| 4. #23761464 | C2 | semidirect |
| 5. #23761380 | C2 | semidirect |
| 7. C8×C16×C79 | C2 | semidirect |
| 47. #11929613 | C16 | direct (N × H) |
| 67. C16×C79 | SD16 | semidirect |
| 80. Dic158 | C2×C16 | semidirect |
| 84. C8×C79 | C2×C16 | semidirect |
| 112. C8×C16 | D79 | semidirect |
| 113. C79 | C16×SD16 | semidirect |
| 173. C16 | #11929613 | direct (N × H) |
| 192. C8 | C16×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic158 | 2 |
| C16×D316 | 2 |
| C8×#11929613 | 2 |
| #23761464 | 2 |
| #23761380 | 2 |
| #23761356 | 2 |
| C8×C16×C79 | 2 |
| C16×SD16 | 79 |