Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
232 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×#17985839 | C2 | semidirect |
| 5. #22590591 | C2 | semidirect |
| 6. #22586473 | C2 | semidirect |
| 7. C2×Q64×C71 | C2 | semidirect |
| 99. C2×Q64 | D71 | semidirect |
| 105. C71 | #13730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985839 | 2 |
| C2×#17985838 | 2 |
| C2×#17985836 | 2 |
| #22590602 | 2 |
| #22590591 | 2 |
| #22586473 | 2 |
| C2×Q64×C71 | 2 |
| #13730 | 71 |