Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
408 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 91 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×#17985826 | C2 | semidirect |
| 3. C2×#17985805 | C2 | semidirect |
| 4. #22590053 | C2 | semidirect |
| 5. C2×#17985784 | C2 | semidirect |
| 6. #22588401 | C2 | semidirect |
| 7. C71×#1387 | C2 | semidirect |
| 51. C2×C71⋊C16 | D4 | semidirect |
| 190. #1387 | D71 | semidirect |
| 191. C71 | #13385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598012 | 2 |
| C2×#17985826 | 2 |
| C2×#17985805 | 2 |
| #22590053 | 2 |
| C2×#17985784 | 2 |
| #22588401 | 2 |
| C71×#1387 | 2 |
| #13385 | 71 |