Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 101 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. #23765202 | C2 | semidirect |
| 3. C4×#14579100 | C2 | semidirect |
| 4. Q8⋊(C79⋊C16) | C2 | semidirect |
| 5. #23761356 | C2 | semidirect |
| 6. #23761354 | C2 | semidirect |
| 7. C79×Q8⋊C16 | C2 | semidirect |
| 105. Q8×C79 | M32 | semidirect |
| 117. D316 | M32 | semidirect |
| 162. Q8⋊C16 | D79 | semidirect |
| 165. C79 | #11615 | semidirect |
| 263. Q8 | #14579100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#11929625 | 2 |
| #23765202 | 2 |
| C4×#14579100 | 2 |
| Q8⋊(C79⋊C16) | 2 |
| #23761356 | 2 |
| #23761354 | 2 |
| C79×Q8⋊C16 | 2 |
| #11615 | 79 |