Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#17986434 | C2 | semidirect |
| 2. C2×#17986269 | C2 | semidirect |
| 3. C2×#17985806 | C2 | semidirect |
| 4. C2×#17985799 | C2 | semidirect |
| 5. C2×#17985783 | C2 | semidirect |
| 6. #22586448 | C2 | semidirect |
| 7. C71×#3061 | C2 | semidirect |
| 40. C2×D568 | D4 | semidirect |
| 46. #14556068 | D4 | semidirect |
| 52. #14556064 | D4 | semidirect |
| 221. #3061 | D71 | semidirect |
| 226. C71 | #13307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986434 | 2 |
| C2×#17986269 | 2 |
| C2×#17985806 | 2 |
| C2×#17985799 | 2 |
| C2×#17985783 | 2 |
| #22586448 | 2 |
| C71×#3061 | 2 |
| #13307 | 71 |