Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
346 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 346 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. #22590565 | C2 | semidirect |
| 2. #22590375 | C2 | semidirect |
| 3. #22587695 | C2 | semidirect |
| 4. #22586395 | C2 | semidirect |
| 5. #22586301 | C2 | semidirect |
| 6. D4⋊(C71⋊C16) | C2 | semidirect |
| 7. C71×#3334 | C2 | semidirect |
| 97. D4×C71 | D16 | semidirect |
| 144. #3334 | D71 | semidirect |
| 151. C71 | #12340 | semidirect |
| 246. D4 | #14556069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590565 | 2 |
| #22590375 | 2 |
| #22587695 | 2 |
| #22586395 | 2 |
| #22586301 | 2 |
| D4⋊(C71⋊C16) | 2 |
| C71×#3334 | 2 |
| #12340 | 71 |