Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
242 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 85 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. C16×D316 | C2 | semidirect |
| 3. #23761463 | C2 | semidirect |
| 4. D4⋊(C79⋊C16) | C2 | semidirect |
| 5. #23761354 | C2 | semidirect |
| 6. #23761319 | C2 | semidirect |
| 7. C79×#2169 | C2 | semidirect |
| 83. D316 | M32 | semidirect |
| 114. #2169 | D79 | semidirect |
| 121. C79 | #12063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D316 | 2 |
| C8×#11929609 | 2 |
| #23761463 | 2 |
| D4⋊(C79⋊C16) | 2 |
| #23761354 | 2 |
| #23761319 | 2 |
| C79×#2169 | 2 |
| #12063 | 79 |