Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23765650 | C2 | semidirect |
| 2. #23765649 | C2 | semidirect |
| 3. #23763014 | C2 | semidirect |
| 4. C16×C79⋊C8 | C2 | semidirect |
| 5. C79×#2246 | C2 | semidirect |
| 35. C79⋊C16 | D8 | semidirect |
| 43. C16×C79 | D8 | semidirect |
| 56. C79⋊C8 | D16 | semidirect |
| 72. #2246 | D79 | semidirect |
| 75. C79 | #12515 | semidirect |
| 113. C16 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765650 | 2 |
| #23765649 | 2 |
| #23763014 | 2 |
| C16×C79⋊C8 | 2 |
| C79×#2246 | 2 |
| #12515 | 79 |