Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
330 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 2. C2×#17985833 | C2 | semidirect |
| 3. (C2×D71)⋊C32 | C2 | semidirect |
| 4. C2×M64×C71 | C2 | semidirect |
| 12. C2×C71⋊C32 | C22 | semidirect |
| 15. C2×C32×C71 | C22 | semidirect |
| 77. C2×D71 | M64 | semidirect |
| 89. C2×M64 | D71 | semidirect |
| 91. C71 | #13553 | semidirect |
| 102. C2×C32 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D71 | 2 |
| C2×#17985833 | 2 |
| (C2×D71)⋊C32 | 2 |
| C2×M64×C71 | 2 |
| #13553 | 71 |