Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
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. #22586409 | C2 | semidirect |
| 4. Q8⋊(C71⋊C16) | C2 | semidirect |
| 6. #22586259 | C2 | semidirect |
| 7. Q8×C16×C71 | C2 | semidirect |
| 46. #11765852 | C16 | semidirect |
| 70. Q8×C71 | C2×C16 | semidirect |
| 88. C71⋊C8 | C2×C16 | semidirect |
| 106. Q8×C16 | D71 | semidirect |
| 113. C71 | SD16⋊C16 | semidirect |
| 176. Q8 | C16×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D284 | 2 |
| C8×#11765852 | 2 |
| #22586409 | 2 |
| Q8⋊(C71⋊C16) | 2 |
| #22586294 | 2 |
| #22586259 | 2 |
| Q8×C16×C71 | 2 |
| SD16⋊C16 | 71 |