Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
262 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23761472 | C2 | semidirect |
| 4. #23761471 | C2 | semidirect |
| 5. C79×#1371 | C2 | semidirect |
| 24. C16×D79 | C8 | semidirect |
| 48. C79⋊C16 | C2×C8 | semidirect |
| 54. C16×C79 | C2×C8 | semidirect |
| 90. D79 | #1371 | direct (N × H) |
| 95. #1371 | D79 | direct (N × H) |
| 96. C79 | C2×#1371 | semidirect |
| 145. C16 | C8×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C16×D79 | 2 |
| #335×D79 | 2 |
| #23761472 | 2 |
| #23761471 | 2 |
| C79×#1371 | 2 |
| C2×#1371 | 79 |