Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
550 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22598685 | C2 | semidirect |
| 2. #22598349 | C2 | semidirect |
| 4. #22589137 | C2 | semidirect |
| 5. #22586742 | C2 | semidirect |
| 6. #22586170 | C2 | semidirect |
| 7. C71×#1480 | C2 | semidirect |
| 211. #1480 | D71 | semidirect |
| 213. C71 | #10033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598685 | 2 |
| #22598349 | 2 |
| #22598336 | 2 |
| #22589137 | 2 |
| #22586742 | 2 |
| #22586170 | 2 |
| C71×#1480 | 2 |
| #10033 | 71 |