Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
828 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#19098758 | C2 | semidirect |
| 2. #23764205 | C2 | semidirect |
| 3. C2×D4⋊(C79⋊C8) | C2 | semidirect |
| 4. #23761283 | C2 | semidirect |
| 5. C79×#2537 | C2 | semidirect |
| 29. #14579158 | D4 | semidirect |
| 31. C4⋊(C79⋊C8) | D4 | semidirect |
| 77. C2×D4×C79 | D8 | semidirect |
| 178. #2537 | D79 | semidirect |
| 182. C79 | #10228 | semidirect |
| 247. C2×D4 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098758 | 2 |
| #23764205 | 2 |
| C2×D4⋊(C79⋊C8) | 2 |
| #23761283 | 2 |
| C79×#2537 | 2 |
| #10228 | 79 |