Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
244 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 244 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 |
|---|---|---|
| 2. #22587700 | C2 | semidirect |
| 3. #22586414 | C2 | semidirect |
| 4. #22586387 | C2 | semidirect |
| 5. C71×#2183 | C2 | semidirect |
| 51. C16×C71 | SD16 | semidirect |
| 85. #2183 | D71 | semidirect |
| 89. C71 | #12442 | semidirect |
| 135. C16 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590590 | 2 |
| #22587700 | 2 |
| #22586414 | 2 |
| #22586387 | 2 |
| C71×#2183 | 2 |
| #12442 | 71 |