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 |
|---|---|---|
| 2. C4×C4⋊(C71⋊C8) | C2 | semidirect |
| 3. #22587115 | C2 | semidirect |
| 6. #22586236 | C2 | semidirect |
| 7. C71×#1276 | C2 | semidirect |
| 17. #17985744 | C4 | semidirect |
| 18. #17985742 | C4 | semidirect |
| 162. #1276 | D71 | semidirect |
| 163. C71 | #9577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589168 | 2 |
| C4×C4⋊(C71⋊C8) | 2 |
| #22587115 | 2 |
| #22586987 | 2 |
| #22586740 | 2 |
| #22586236 | 2 |
| C71×#1276 | 2 |
| #9577 | 71 |