Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
242 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. C8×Dic284 | C2 | semidirect |
| 3. #22586413 | C2 | semidirect |
| 4. #22586303 | C2 | semidirect |
| 6. C8×C71⋊C16 | C2 | semidirect |
| 25. #14556072 | C8 | direct (N × H) |
| 46. Dic284 | C2×C8 | semidirect |
| 53. C71⋊C16 | C2×C8 | semidirect |
| 85. C8×C71 | SD32 | semidirect |
| 113. C71 | C8×SD32 | semidirect |
| 192. C8 | #14556072 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556072 | 2 |
| C8×Dic284 | 2 |
| #22586413 | 2 |
| #22586303 | 2 |
| #22586301 | 2 |
| C8×C71⋊C16 | 2 |
| C8×D8×C71 | 2 |
| C8×SD32 | 71 |