Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
636 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22598785 | C2 | semidirect |
| 2. #22598340 | C2 | semidirect |
| 3. #22589139 | C2 | semidirect |
| 4. #22586740 | C2 | semidirect |
| 5. #22586739 | C2 | semidirect |
| 6. #22586170 | C2 | semidirect |
| 7. C71×#3100 | C2 | semidirect |
| 103. C2×C71⋊C8 | D8 | semidirect |
| 224. #3100 | D71 | semidirect |
| 229. C71 | #10032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598785 | 2 |
| #22598340 | 2 |
| #22589139 | 2 |
| #22586740 | 2 |
| #22586739 | 2 |
| #22586170 | 2 |
| C71×#3100 | 2 |
| #10032 | 71 |