Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
224 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23761316 | C2 | semidirect |
| 7. C79×Q8⋊C16 | C2 | semidirect |
| 57. C79⋊C16 | SD16 | semidirect |
| 70. Q8×C79 | M32 | semidirect |
| 110. Q8⋊C16 | D79 | semidirect |
| 113. C79 | #12050 | semidirect |
| 176. Q8 | #14579100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C79⋊C16 | 2 |
| #23765231 | 2 |
| C8×#11929611 | 2 |
| #23761463 | 2 |
| #23761356 | 2 |
| #23761316 | 2 |
| C79×Q8⋊C16 | 2 |
| #12050 | 79 |