Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22589115 | C2 | semidirect |
| 3. #22587111 | C2 | semidirect |
| 6. #22586215 | C2 | semidirect |
| 7. C71×#1565 | C2 | semidirect |
| 161. #1565 | D71 | semidirect |
| 165. C71 | #10607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589180 | 2 |
| #22589115 | 2 |
| #22587111 | 2 |
| #22587007 | 2 |
| C2×#17985742 | 2 |
| #22586215 | 2 |
| C71×#1565 | 2 |
| #10607 | 71 |