Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
508 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 117 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. C22×C16×D71 | C2 | semidirect |
| 3. C2×#17985807 | C2 | semidirect |
| 4. C2×#17985805 | C2 | semidirect |
| 5. #22588375 | C2 | semidirect |
| 6. #22586435 | C2 | semidirect |
| 7. C71×#1382 | C2 | semidirect |
| 51. C2×C71⋊C16 | D4 | semidirect |
| 63. C2×C16×C71 | D4 | semidirect |
| 166. C2×D71 | #359 | semidirect |
| 187. #1382 | D71 | semidirect |
| 188. C71 | #13063 | semidirect |
| 239. C2×C16 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D71 | 2 |
| #22597922 | 2 |
| C2×#17985807 | 2 |
| C2×#17985805 | 2 |
| #22588375 | 2 |
| #22586435 | 2 |
| C71×#1382 | 2 |
| #13063 | 71 |