Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
218 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22590620 | C2 | semidirect |
| 5. #22586413 | C2 | semidirect |
| 6. #22586394 | C2 | semidirect |
| 7. C71×#1365 | C2 | semidirect |
| 57. C71⋊C16 | SD16 | semidirect |
| 108. #1365 | D71 | semidirect |
| 110. C71 | #12453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590620 | 2 |
| #22590159 | 2 |
| #22587736 | 2 |
| #22587730 | 2 |
| #22586413 | 2 |
| #22586394 | 2 |
| C71×#1365 | 2 |
| #12453 | 71 |