Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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×#17986266 | C2 | semidirect |
| 2. #22598006 | C2 | semidirect |
| 3. C2×#17985806 | C2 | semidirect |
| 4. C2×#17985800 | C2 | semidirect |
| 5. C2×#17985784 | C2 | semidirect |
| 6. #22586449 | C2 | semidirect |
| 7. C2×#509×C71 | C2 | semidirect |
| 54. #14556064 | D4 | semidirect |
| 74. C2×D8×C71 | D4 | semidirect |
| 79. M32×C71 | D4 | semidirect |
| 219. C2×#509 | D71 | semidirect |
| 226. C71 | #13307 | semidirect |
| 269. C2×D8 | C22⋊D71 | semidirect |
| 288. M32 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986266 | 2 |
| #22598006 | 2 |
| C2×#17985806 | 2 |
| C2×#17985800 | 2 |
| C2×#17985784 | 2 |
| #22586449 | 2 |
| C2×#509×C71 | 2 |
| #13307 | 71 |