Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
216 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #23765237 | C2 | semidirect |
| 3. #23765236 | C2 | semidirect |
| 4. #23761475 | C2 | semidirect |
| 5. #23761374 | C2 | semidirect |
| 6. C8×C79⋊C16 | C2 | semidirect |
| 7. C79×#1335 | C2 | semidirect |
| 25. #14579107 | C8 | semidirect |
| 26. #14579105 | C8 | semidirect |
| 27. #14579104 | C8 | semidirect |
| 28. #14579102 | C8 | semidirect |
| 108. #1335 | D79 | semidirect |
| 110. C79 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765279 | 2 |
| #23765237 | 2 |
| #23765236 | 2 |
| #23761475 | 2 |
| #23761374 | 2 |
| C8×C79⋊C16 | 2 |
| C79×#1335 | 2 |
| #12046 | 79 |