Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 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. C4×C4⋊(C71⋊C8) | C2 | semidirect |
| 2. #22587112 | C2 | semidirect |
| 5. #22586235 | C2 | semidirect |
| 6. #22586173 | C2 | semidirect |
| 15. #17985745 | C4 | semidirect |
| 16. #17985743 | C4 | semidirect |
| 163. C71 | #9578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C71⋊C8) | 2 |
| #22587112 | 2 |
| #22586989 | 2 |
| #22586739 | 2 |
| #22586235 | 2 |
| #22586173 | 2 |
| C71×#1962 | 2 |
| #9578 | 71 |