Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
386 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22590139 | C2 | semidirect |
| 3. #22586299 | C2 | semidirect |
| 4. C71×#2163 | C2 | semidirect |
| 13. C4⋊(C71⋊C16) | C22 | semidirect |
| 19. #346×C71 | C22 | semidirect |
| 127. #2163 | D71 | semidirect |
| 130. C71 | #11634 | semidirect |
| 144. #346 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986078 | 2 |
| #22590139 | 2 |
| #22586299 | 2 |
| C71×#2163 | 2 |
| #11634 | 71 |