Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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×#17986415 | C2 | semidirect |
| 3. #22590076 | C2 | semidirect |
| 4. #22588395 | C2 | semidirect |
| 5. #22586451 | C2 | semidirect |
| 6. #22586436 | C2 | semidirect |
| 7. C2×#359×C71 | C2 | semidirect |
| 15. #17986271 | C4 | semidirect |
| 16. #17986266 | C4 | semidirect |
| 184. C2×#359 | D71 | semidirect |
| 188. C71 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986415 | 2 |
| #22598056 | 2 |
| #22590076 | 2 |
| #22588395 | 2 |
| #22586451 | 2 |
| #22586436 | 2 |
| C2×#359×C71 | 2 |
| #13071 | 71 |