Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
232 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23761469 | C2 | semidirect |
| 4. Q8⋊(C79⋊C16) | C2 | semidirect |
| 6. #23761319 | C2 | semidirect |
| 7. Q8×C16×C79 | C2 | semidirect |
| 46. #11929611 | C16 | semidirect |
| 70. Q8×C79 | C2×C16 | semidirect |
| 88. C79⋊C8 | C2×C16 | semidirect |
| 106. Q8×C16 | D79 | semidirect |
| 113. C79 | SD16⋊C16 | semidirect |
| 176. Q8 | C16×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D316 | 2 |
| C8×#11929611 | 2 |
| #23761469 | 2 |
| Q8⋊(C79⋊C16) | 2 |
| #23761354 | 2 |
| #23761319 | 2 |
| Q8×C16×C79 | 2 |
| SD16⋊C16 | 79 |