Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
248 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22590242 | C2 | semidirect |
| 3. #22587701 | C2 | semidirect |
| 4. #22587697 | C2 | semidirect |
| 5. #22586411 | C2 | semidirect |
| 6. #22586387 | C2 | semidirect |
| 7. C71×#1361 | C2 | semidirect |
| 60. C71⋊C16 | SD16 | semidirect |
| 90. Dic142 | D16 | semidirect |
| 123. #1361 | D71 | semidirect |
| 124. C71 | #12439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590589 | 2 |
| #22590242 | 2 |
| #22587701 | 2 |
| #22587697 | 2 |
| #22586411 | 2 |
| #22586387 | 2 |
| C71×#1361 | 2 |
| #12439 | 71 |