Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
304 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 71 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. Q16×Dic142 | C2 | semidirect |
| 5. #22586399 | C2 | semidirect |
| 6. #22586320 | C2 | semidirect |
| 7. C71×#1332 | C2 | semidirect |
| 75. Q16×C71 | SD16 | semidirect |
| 103. Dic142 | SD32 | semidirect |
| 134. #1332 | D71 | semidirect |
| 135. C71 | #12354 | semidirect |
| 189. Q16 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic142 | 2 |
| #22590564 | 2 |
| #22590380 | 2 |
| #22587701 | 2 |
| #22586399 | 2 |
| #22586320 | 2 |
| C71×#1332 | 2 |
| #12354 | 71 |