Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
4070 conjugacy classes of subgroups; only the 651 normal subgroups are shown.
This group has 4070 conjugacy classes of subgroups — too many to draw. Only its 651 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. C22×C22⋊(C71⋊C8) | C2 | semidirect |
| 2. #22588252 | C2 | direct (N × H) |
| 6. C2×C22⋊(C71⋊C8) | C22 | semidirect |
| 89. C2×C71 | #1780 | semidirect |
| 95. C71 | C2×#1780 | semidirect |
| 180. C2 | #22588252 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊(C71⋊C8) | 2 |
| #22588252 | 2 |
| C23×#41×C71 | 2 |
| C2×#1780 | 71 |