Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 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 |
|---|---|---|
| 1. #22601474 | C2 | semidirect |
| 2. C2×#17986435 | C2 | semidirect |
| 3. #22590076 | C2 | semidirect |
| 4. #22590056 | C2 | semidirect |
| 5. #22589238 | C2 | semidirect |
| 6. #22586426 | C2 | semidirect |
| 7. C71×#3155 | C2 | semidirect |
| 38. C2×Dic284 | D4 | semidirect |
| 40. C2×D568 | D4 | semidirect |
| 51. #14556068 | D4 | semidirect |
| 53. C2×C71⋊C16 | D4 | semidirect |
| 220. #3155 | D71 | semidirect |
| 225. C71 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601474 | 2 |
| C2×#17986435 | 2 |
| #22590076 | 2 |
| #22590056 | 2 |
| #22589238 | 2 |
| #22586426 | 2 |
| C71×#3155 | 2 |
| #13334 | 71 |