Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
498 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22586385 | C2 | semidirect |
| 4. C71×#1567 | C2 | semidirect |
| 12. C4⋊(C71⋊C16) | C22 | semidirect |
| 18. #335×C71 | C22 | semidirect |
| 128. #1567 | D71 | semidirect |
| 130. C71 | #11961 | semidirect |
| 144. #335 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986376 | 2 |
| #22590139 | 2 |
| #22586385 | 2 |
| C71×#1567 | 2 |
| #11961 | 71 |