Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
248 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #22587700 | C2 | semidirect |
| 3. #22586412 | C2 | semidirect |
| 4. #22586387 | C2 | semidirect |
| 5. Q8×C16×C71 | C2 | semidirect |
| 51. C16×C71 | SD16 | semidirect |
| 54. Q8×C71 | D16 | semidirect |
| 87. Q8×C16 | D71 | semidirect |
| 91. C71 | #12439 | semidirect |
| 137. C16 | #11765852 | semidirect |
| 140. Q8 | D1136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590590 | 2 |
| #22587700 | 2 |
| #22586412 | 2 |
| #22586387 | 2 |
| Q8×C16×C71 | 2 |
| #12439 | 71 |