Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
344 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4⋊#3633 | C2 | semidirect |
| 2. C2×C4×#3633 | C2 | semidirect |
| 3. D4⋊#3633 | C2 | direct (N × H) |
| 17. C4⋊#3633 | C22 | semidirect |
| 19. C4×#3633 | C22 | semidirect |
| 32. C2×D4×C17 | C8 | semidirect |
| 36. D4×D17 | C8 | semidirect |
| 38. C2×D68 | C8 | semidirect |
| 70. D4×C17 | C2×C8 | semidirect |
| 76. D68 | C2×C8 | semidirect |
| 109. C2×C17 | D4⋊C8 | semidirect |
| 112. D17 | D4⋊C8 | semidirect |
| 130. C17 | C2×D4⋊C8 | semidirect |
| 138. C2×D4 | #3633 | semidirect |
| 171. D4 | C2×#3633 | semidirect |
| 219. C2 | D4⋊#3633 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#3633 | 2 |
| C2×C4×#3633 | 2 |
| D4⋊#3633 | 2 |
| C2×D4×#595 | 2 |
| C2×D4⋊C8 | 17 |