Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22590565 | C2 | semidirect |
| 3. #22587700 | C2 | semidirect |
| 4. #22586395 | C2 | semidirect |
| 5. Q8⋊(C71⋊C16) | C2 | semidirect |
| 6. #22586301 | C2 | semidirect |
| 7. Q8×D8×C71 | C2 | semidirect |
| 72. D8×C71 | SD16 | semidirect |
| 92. Q8×C71 | D16 | semidirect |
| 137. Q8×D8 | D71 | semidirect |
| 144. C71 | #12352 | semidirect |
| 206. D8 | #11765852 | semidirect |
| 229. Q8 | #14556069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590565 | 2 |
| #22590375 | 2 |
| #22587700 | 2 |
| #22586395 | 2 |
| Q8⋊(C71⋊C16) | 2 |
| #22586301 | 2 |
| Q8×D8×C71 | 2 |
| #12352 | 71 |