Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
640 conjugacy classes of subgroups; only the 378 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 378 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⋊#3624 | C2 | direct (N × H) |
| 11. C4⋊#3624 | C22 | direct (N × H) |
| 13. C22×C4×C17 | C8 | semidirect |
| 29. C2×C4×C17 | C2×C8 | semidirect |
| 40. C22×C17 | C4⋊C8 | semidirect |
| 45. C4×C17 | C22×C8 | semidirect |
| 53. C2×C17 | C2×C4⋊C8 | semidirect |
| 65. C17 | C22×C4⋊C8 | semidirect |
| 73. C22×C4 | #3624 | semidirect |
| 90. C2×C4 | C2×#3624 | semidirect |
| 93. C22 | C4⋊#3624 | direct (N × H) |
| 102. C4 | C22×#3624 | semidirect |
| 103. C2 | C2×C4⋊#3624 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3624 | 2 |
| C2×C4⋊#3624 | 2 |
| C22×C4×Dic17 | 2 |
| C22×C4⋊C8 | 17 |