Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1230 conjugacy classes of subgroups; only the 427 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 427 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 |
|---|---|---|
| 3. #23763554 | C2 | semidirect |
| 4. #23763553 | C2 | semidirect |
| 5. C79×#1843 | C2 | semidirect |
| 75. D79 | #1843 | direct (N × H) |
| 80. #1843 | D79 | direct (N × H) |
| 81. C79 | C2×#1843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C8×D79 | 2 |
| #376×D79 | 2 |
| #23763554 | 2 |
| #23763553 | 2 |
| C79×#1843 | 2 |
| C2×#1843 | 79 |