Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
494 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22587098 | C2 | semidirect |
| 4. #22587012 | C2 | semidirect |
| 6. M16×C71⋊C8 | C2 | semidirect |
| 7. C71×#1966 | C2 | semidirect |
| 155. #1966 | D71 | semidirect |
| 161. C71 | #9796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986347 | 2 |
| #22589180 | 2 |
| #22587098 | 2 |
| #22587012 | 2 |
| #22587009 | 2 |
| M16×C71⋊C8 | 2 |
| C71×#1966 | 2 |
| #9796 | 71 |