Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. C2×C4×#3633 | C2 | semidirect |
| 4. (C2×#3633)⋊C4 | C2 | semidirect |
| 8. C22×#3633 | C4 | semidirect |
| 14. C22⋊#3633 | C4 | semidirect |
| 35. C22⋊#595 | C8 | semidirect |
| 38. C22⋊C4×C17 | C8 | semidirect |
| 39. C22⋊Dic17 | C8 | semidirect |
| 40. #63227 | C8 | semidirect |
| 55. C2×#595 | C2×C8 | semidirect |
| 62. #3633 | C22⋊C4 | direct (N × H) |
| 63. C2×C4×C17 | C2×C8 | semidirect |
| 64. C2×Dic17 | C2×C8 | semidirect |
| 69. C22×C17 | C4×C8 | semidirect |
| 75. C2×D17 | C4×C8 | semidirect |
| 111. C17 | C8×C22⋊C4 | semidirect |
| 132. C22⋊C4 | #3633 | direct (N × H) |
| 157. C2×C4 | C2×#3633 | semidirect |
| 171. C22 | C4×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3633 | 2 |
| C2×C22⋊#3633 | 2 |
| C2×C4×#3633 | 2 |
| (C2×#3633)⋊C4 | 2 |
| C22⋊C4×#595 | 2 |
| C8×C22⋊C4 | 17 |