Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
348 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22589333 | C2 | semidirect |
| 3. #22587108 | C2 | semidirect |
| 5. #22586943 | C2 | semidirect |
| 7. C71×#1291 | C2 | semidirect |
| 172. #1291 | D71 | semidirect |
| 173. C71 | #10497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599532 | 2 |
| #22589333 | 2 |
| #22587108 | 2 |
| #22587063 | 2 |
| #22586943 | 2 |
| #22586931 | 2 |
| C71×#1291 | 2 |
| #10497 | 71 |