Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
328 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 103 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×#17985820 | C2 | semidirect |
| 4. C2×#17985776 | C2 | semidirect |
| 6. #22586419 | C2 | semidirect |
| 7. C71×#1376 | C2 | semidirect |
| 155. #1376 | D71 | semidirect |
| 157. C71 | #13128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985820 | 2 |
| C2×#17985780 | 2 |
| C2×#17985776 | 2 |
| #22588123 | 2 |
| #22586419 | 2 |
| C71×#1376 | 2 |
| #13128 | 71 |