Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
254 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23761466 | C2 | semidirect |
| 4. #23761465 | C2 | semidirect |
| 5. C79×#1368 | C2 | semidirect |
| 24. C16×D79 | C8 | semidirect |
| 46. C79⋊C16 | C2×C8 | semidirect |
| 52. C16×C79 | C2×C8 | semidirect |
| 79. D79 | #1368 | direct (N × H) |
| 84. #1368 | D79 | direct (N × H) |
| 85. C79 | C2×#1368 | semidirect |
| 132. C16 | C8×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #346×D79 | 2 |
| #334×D79 | 2 |
| #23761466 | 2 |
| #23761465 | 2 |
| C79×#1368 | 2 |
| C2×#1368 | 79 |