Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
478 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17986417 | C2 | semidirect |
| 3. C2×#17985813 | C2 | semidirect |
| 4. C2×#17985799 | C2 | semidirect |
| 5. #22588405 | C2 | semidirect |
| 6. #22586433 | C2 | semidirect |
| 7. C71×#1387 | C2 | semidirect |
| 17. #17986270 | C4 | semidirect |
| 183. #1387 | D71 | semidirect |
| 185. C71 | #13073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986417 | 2 |
| C2×#17986270 | 2 |
| C2×#17985813 | 2 |
| C2×#17985799 | 2 |
| #22588405 | 2 |
| #22586433 | 2 |
| C71×#1387 | 2 |
| #13073 | 71 |