Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
222 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 222 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 |
|---|---|---|
| 1. Q8×C71⋊C16 | C2 | semidirect |
| 3. #22586410 | C2 | semidirect |
| 4. Q8⋊(C71⋊C16) | C2 | semidirect |
| 6. #22586258 | C2 | semidirect |
| 70. Q8×C71 | M32 | semidirect |
| 113. C71 | #12056 | semidirect |
| 176. Q8 | #14556068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C71⋊C16 | 2 |
| #22590172 | 2 |
| #22586410 | 2 |
| Q8⋊(C71⋊C16) | 2 |
| D4⋊(C71⋊C16) | 2 |
| #22586258 | 2 |
| C8×SD16×C71 | 2 |
| #12056 | 71 |