Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
238 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 238 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 |
|---|---|---|
| 1. Q8×C79⋊C16 | C2 | semidirect |
| 4. #23761463 | C2 | semidirect |
| 6. C16×C79⋊C8 | C2 | semidirect |
| 7. C79×Q8⋊C16 | C2 | semidirect |
| 46. #11929611 | C16 | semidirect |
| 57. C79⋊C16 | SD16 | semidirect |
| 70. Q8×C79 | C2×C16 | semidirect |
| 88. C79⋊C8 | C2×C16 | semidirect |
| 110. Q8⋊C16 | D79 | semidirect |
| 113. C79 | C16×SD16 | 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 |
|---|---|
| Q8×C79⋊C16 | 2 |
| #23765219 | 2 |
| C8×#11929611 | 2 |
| #23761463 | 2 |
| #23761356 | 2 |
| C16×C79⋊C8 | 2 |
| C79×Q8⋊C16 | 2 |
| C16×SD16 | 79 |