Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 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. #22601476 | C2 | semidirect |
| 2. C2×#17986435 | C2 | semidirect |
| 3. #22598821 | C2 | semidirect |
| 4. #22590075 | C2 | semidirect |
| 5. #22589236 | C2 | semidirect |
| 6. #22586425 | C2 | semidirect |
| 7. C71×#2140 | C2 | semidirect |
| 46. C2×Dic284 | D4 | semidirect |
| 51. C2×D568 | D4 | semidirect |
| 66. #14556068 | D4 | semidirect |
| 83. C2×C16×C71 | D4 | semidirect |
| 222. #2140 | D71 | semidirect |
| 225. C71 | #13334 | semidirect |
| 297. C2×C16 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601476 | 2 |
| C2×#17986435 | 2 |
| #22598821 | 2 |
| #22590075 | 2 |
| #22589236 | 2 |
| #22586425 | 2 |
| C71×#2140 | 2 |
| #13334 | 71 |