Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
202 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 91 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×#17985832 | C2 | semidirect |
| 3. C4⋊(C71⋊C32) | C2 | semidirect |
| 4. (C2×D71)⋊C32 | C2 | semidirect |
| 5. C4×C32×C71 | C2 | semidirect |
| 27. C32×C71 | D4 | semidirect |
| 59. C4×C71 | M64 | semidirect |
| 72. C4×C32 | D71 | semidirect |
| 73. C71 | #13646 | semidirect |
| 95. C32 | D284 | semidirect |
| 128. C4 | #17985832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985832 | 2 |
| C16×D284 | 2 |
| C4⋊(C71⋊C32) | 2 |
| (C2×D71)⋊C32 | 2 |
| C4×C32×C71 | 2 |
| #13646 | 71 |