Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
380 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#17985823 | C2 | semidirect |
| 3. C2×#17985822 | C2 | semidirect |
| 6. #22586451 | C2 | semidirect |
| 7. C71×#1385 | C2 | semidirect |
| 19. #17985782 | C4 | semidirect |
| 146. #1385 | D71 | semidirect |
| 147. C71 | #12933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596948 | 2 |
| C2×#17985823 | 2 |
| C2×#17985822 | 2 |
| #22589967 | 2 |
| #22588396 | 2 |
| #22586451 | 2 |
| C71×#1385 | 2 |
| #12933 | 71 |