Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
770 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 255 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 |
|---|---|---|
| 3. #22588514 | C2 | semidirect |
| 4. #22588481 | C2 | semidirect |
| 6. #22588245 | C2 | semidirect |
| 7. C71×#1838 | C2 | semidirect |
| 112. #1838 | D71 | semidirect |
| 115. C71 | #20830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596972 | 2 |
| C2×#97×D71 | 2 |
| #22588514 | 2 |
| #22588481 | 2 |
| #22588377 | 2 |
| #22588245 | 2 |
| C71×#1838 | 2 |
| #20830 | 71 |