Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
216 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 216 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. #23765237 | C2 | semidirect |
| 2. #23761476 | C2 | semidirect |
| 3. #23761373 | C2 | semidirect |
| 4. C16×C79⋊C8 | C2 | semidirect |
| 24. Q32×C79 | C8 | semidirect |
| 25. SD32×C79 | C8 | semidirect |
| 26. D16×C79 | C8 | semidirect |
| 77. C79 | #12046 | semidirect |
| 90. Q32 | C79⋊C8 | semidirect |
| 91. SD32 | C79⋊C8 | semidirect |
| 92. D16 | C79⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765237 | 2 |
| #23761476 | 2 |
| #23761373 | 2 |
| C16×C79⋊C8 | 2 |
| C79×#2178 | 2 |
| #12046 | 79 |