Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
566 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 566 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. C22×#14556071 | C2 | semidirect |
| 3. C2×#17985813 | C2 | semidirect |
| 4. C2×#17985806 | C2 | semidirect |
| 5. #22589256 | C2 | semidirect |
| 6. #22586430 | C2 | semidirect |
| 7. C2×#510×C71 | C2 | semidirect |
| 52. C2×C71⋊C16 | D4 | semidirect |
| 71. C2×Q16×C71 | D4 | semidirect |
| 78. M32×C71 | D4 | semidirect |
| 202. C2×#510 | D71 | semidirect |
| 209. C71 | #13338 | semidirect |
| 248. C2×Q16 | C22⋊D71 | semidirect |
| 271. M32 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556071 | 2 |
| #22598827 | 2 |
| C2×#17985813 | 2 |
| C2×#17985806 | 2 |
| #22589256 | 2 |
| #22586430 | 2 |
| C2×#510×C71 | 2 |
| #13338 | 71 |