Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 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×C4⋊#3633 | C2 | semidirect |
| 2. C2×C22⋊#3633 | C2 | semidirect |
| 3. C2×C4×#3633 | C2 | semidirect |
| 29. C2×#3633 | D4 | semidirect |
| 30. C2×D4×C17 | C8 | semidirect |
| 31. C2×C22⋊D17 | C8 | semidirect |
| 34. C2×D68 | C8 | semidirect |
| 85. C4×C17 | C22⋊C8 | semidirect |
| 86. Dic17 | C22⋊C8 | semidirect |
| 110. C17 | #1954 | semidirect |
| 116. C2×D4 | #3633 | semidirect |
| 179. C4 | C22⋊#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#3633 | 2 |
| C2×C22⋊#3633 | 2 |
| C2×C4×#3633 | 2 |
| C2×D4×#595 | 2 |
| #1954 | 17 |