Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
436 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 133 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×C4×#3633 | C2 | semidirect |
| 3. (C2×#3633)⋊C4 | C2 | semidirect |
| 14. C22⋊#3633 | C4 | direct (N × H) |
| 21. C22×#595 | C8 | semidirect |
| 29. C2×#3633 | C2×C4 | semidirect |
| 30. C22×C4×C17 | C8 | semidirect |
| 31. C22×Dic17 | C8 | semidirect |
| 34. C2×C4×D17 | C8 | semidirect |
| 35. C2×C4×D17 | C8 | semidirect |
| 81. C22×C17 | C4×C8 | semidirect |
| 89. C2×D17 | C4×C8 | semidirect |
| 98. #595 | C22⋊C8 | semidirect |
| 101. C4×C17 | C22⋊C8 | semidirect |
| 103. Dic17 | C22⋊C8 | semidirect |
| 128. C17 | C4×C22⋊C8 | semidirect |
| 147. C22×C4 | #3633 | semidirect |
| 206. C22 | C4×#3633 | semidirect |
| 215. C4 | C22⋊#3633 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#3633 | 2 |
| C2×C4×#3633 | 2 |
| (C2×#3633)⋊C4 | 2 |
| C22×C4×#595 | 2 |
| C4×C22⋊C8 | 17 |