Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22590375 | C2 | semidirect |
| 2. #22587954 | C2 | semidirect |
| 3. D8×C71⋊C8 | C2 | semidirect |
| 4. #22586409 | C2 | semidirect |
| 5. #22586387 | C2 | semidirect |
| 6. #22586386 | C2 | semidirect |
| 7. C71×#2206 | C2 | semidirect |
| 70. D8×C71 | D8 | semidirect |
| 104. C71⋊C8 | D16 | semidirect |
| 129. #2206 | D71 | semidirect |
| 135. C71 | #12424 | semidirect |
| 192. D8 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590375 | 2 |
| #22587954 | 2 |
| D8×C71⋊C8 | 2 |
| #22586409 | 2 |
| #22586387 | 2 |
| #22586386 | 2 |
| C71×#2206 | 2 |
| #12424 | 71 |