Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
712 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 133 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×#17986290 | C2 | semidirect |
| 3. #22589141 | C2 | semidirect |
| 4. C2×#17985726 | C2 | semidirect |
| 5. C71×#1296 | C2 | semidirect |
| 27. #14556128 | D4 | semidirect |
| 48. C4⋊C8×C71 | D4 | semidirect |
| 163. #1296 | D71 | semidirect |
| 164. C71 | #10235 | semidirect |
| 203. C4⋊C8 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986290 | 2 |
| #22593256 | 2 |
| #22589141 | 2 |
| C2×#17985726 | 2 |
| C71×#1296 | 2 |
| #10235 | 71 |