Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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. C16×D284 | C2 | semidirect |
| 3. #22586410 | C2 | semidirect |
| 4. #22586296 | C2 | semidirect |
| 5. C8×C16×C71 | C2 | semidirect |
| 33. D568 | C16 | direct (N × H) |
| 48. C16×C71 | D8 | semidirect |
| 55. D284 | C2×C16 | semidirect |
| 61. C8×C71 | C2×C16 | semidirect |
| 84. C8×C16 | D71 | semidirect |
| 85. C71 | C16×D8 | semidirect |
| 128. C16 | D568 | direct (N × H) |
| 142. C8 | C16×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D284 | 2 |
| C8×D568 | 2 |
| #22586410 | 2 |
| #22586296 | 2 |
| C8×C16×C71 | 2 |
| C16×D8 | 71 |