Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
390 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22590597 | C2 | semidirect |
| 2. #22590375 | C2 | semidirect |
| 3. #22587695 | C2 | semidirect |
| 4. #22586389 | C2 | semidirect |
| 5. #22586301 | C2 | semidirect |
| 6. D4⋊(C71⋊C16) | C2 | semidirect |
| 7. C71×#3283 | C2 | semidirect |
| 80. D8×C71 | D8 | semidirect |
| 151. #3283 | D71 | semidirect |
| 158. C71 | #12319 | semidirect |
| 228. D8 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590597 | 2 |
| #22590375 | 2 |
| #22587695 | 2 |
| #22586389 | 2 |
| #22586301 | 2 |
| D4⋊(C71⋊C16) | 2 |
| C71×#3283 | 2 |
| #12319 | 71 |