Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
338 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22590525 | C2 | semidirect |
| 3. #22590520 | C2 | semidirect |
| 4. #22586354 | C2 | semidirect |
| 5. #22586354 | C2 | semidirect |
| 6. #22586266 | C2 | semidirect |
| 7. C71×#2078 | C2 | semidirect |
| 20. C22⋊(C71⋊C16) | C22 | semidirect |
| 21. C22⋊(C71⋊C16) | C22 | semidirect |
| 22. C2×#107×C71 | C22 | semidirect |
| 26. #341×C71 | C22 | semidirect |
| 167. #2078 | D71 | semidirect |
| 171. C71 | #12284 | semidirect |
| 180. C2×#107 | C2×D71 | semidirect |
| 190. #341 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599205 | 2 |
| #22590525 | 2 |
| #22590520 | 2 |
| #22586354 | 2 |
| #22586266 | 2 |
| C71×#2078 | 2 |
| #12284 | 71 |