Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1372 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1372 conjugacy classes of subgroups — too many to draw. Only its 203 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 |
|---|---|---|
| 1. C2×#17986630 | C2 | semidirect |
| 3. #22587279 | C2 | direct (N × H) |
| 4. C2×#17985735 | C2 | semidirect |
| 5. C2×#17985725 | C2 | semidirect |
| 10. #17986630 | C22 | semidirect |
| 20. #17985735 | C22 | semidirect |
| 21. #17985725 | C22 | semidirect |
| 126. C22×C4×C71 | SD16 | semidirect |
| 181. C2×C4×C71 | C2×SD16 | semidirect |
| 225. C2×C71 | #1599 | semidirect |
| 235. C71 | C2×#1599 | semidirect |
| 341. C22×C4 | #11765853 | semidirect |
| 417. C2×C4 | C2×#11765853 | semidirect |
| 453. C2 | #22587279 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986630 | 2 |
| C2×#17986150 | 2 |
| #22587279 | 2 |
| C2×#17985735 | 2 |
| C2×#17985725 | 2 |
| C2×#394×C71 | 2 |
| C2×#1599 | 71 |