Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
534 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 95 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×#17986437 | C2 | semidirect |
| 2. #22598061 | C2 | semidirect |
| 3. C2×#17986270 | C2 | semidirect |
| 4. C2×#17985811 | C2 | semidirect |
| 5. #22590067 | C2 | semidirect |
| 6. #22589960 | C2 | semidirect |
| 7. C71×#1388 | C2 | semidirect |
| 216. #1388 | D71 | semidirect |
| 217. C71 | #13323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986437 | 2 |
| #22598061 | 2 |
| C2×#17986270 | 2 |
| C2×#17985811 | 2 |
| #22590067 | 2 |
| #22589960 | 2 |
| C71×#1388 | 2 |
| #13323 | 71 |