Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
322 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22590568 | C2 | semidirect |
| 4. #22587711 | C2 | semidirect |
| 5. #22586396 | C2 | semidirect |
| 6. #22586320 | C2 | semidirect |
| 105. Dic142 | SD32 | semidirect |
| 137. C71 | #12356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic142 | 2 |
| #22590568 | 2 |
| #22590385 | 2 |
| #22587711 | 2 |
| #22586396 | 2 |
| #22586320 | 2 |
| C71×#1331 | 2 |
| #12356 | 71 |