Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#17986046 | C2 | semidirect |
| 3. #22590068 | C2 | semidirect |
| 4. C2×#17985780 | C2 | semidirect |
| 5. #22586455 | C2 | semidirect |
| 6. #22586454 | C2 | semidirect |
| 7. C71×#2143 | C2 | semidirect |
| 50. #14556064 | D4 | semidirect |
| 70. #108×C71 | D4 | semidirect |
| 188. #2143 | D71 | semidirect |
| 192. C71 | #12998 | semidirect |
| 251. #108 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597945 | 2 |
| C2×#17986046 | 2 |
| #22590068 | 2 |
| C2×#17985780 | 2 |
| #22586455 | 2 |
| #22586454 | 2 |
| C71×#2143 | 2 |
| #12998 | 71 |