Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22586412 | C2 | semidirect |
| 4. #22586395 | C2 | semidirect |
| 5. C71×#2252 | C2 | semidirect |
| 49. C16×C71 | SD16 | semidirect |
| 83. #2252 | D71 | semidirect |
| 88. C71 | #12451 | semidirect |
| 132. C16 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D284 | 2 |
| #22587726 | 2 |
| #22586412 | 2 |
| #22586395 | 2 |
| C71×#2252 | 2 |
| #12451 | 71 |