Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
368 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22587086 | C2 | semidirect |
| 4. #22586171 | C2 | semidirect |
| 5. C71×#1275 | C2 | semidirect |
| 149. #1275 | D71 | semidirect |
| 150. C71 | #8603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986061 | 2 |
| #22587086 | 2 |
| #22586652 | 2 |
| #22586171 | 2 |
| C71×#1275 | 2 |
| #8603 | 71 |