Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
536 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#17986440 | C2 | semidirect |
| 3. #22590076 | C2 | semidirect |
| 4. #22590060 | C2 | semidirect |
| 5. #22589238 | C2 | semidirect |
| 6. #22586426 | C2 | semidirect |
| 7. C71×#3156 | C2 | semidirect |
| 214. #3156 | D71 | semidirect |
| 219. C71 | #13335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601474 | 2 |
| C2×#17986440 | 2 |
| #22590076 | 2 |
| #22590060 | 2 |
| #22589238 | 2 |
| #22586426 | 2 |
| C71×#3156 | 2 |
| #13335 | 71 |