Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
326 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. C2×#17985828 | C2 | semidirect |
| 2. #22590100 | C2 | semidirect |
| 6. #22589123 | C2 | semidirect |
| 7. C71×#1387 | C2 | semidirect |
| 148. #1387 | D71 | semidirect |
| 149. C71 | #13470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985828 | 2 |
| #22590100 | 2 |
| C2×#17985813 | 2 |
| C2×#17985799 | 2 |
| #22589248 | 2 |
| #22589123 | 2 |
| C71×#1387 | 2 |
| #13470 | 71 |