Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
432 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 432 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. C23×#3633 | C2 | semidirect |
| 2. C2×C22⋊#3633 | C2 | semidirect |
| 3. C2×C22⋊#3633 | C2 | semidirect |
| 4. (C2×#3633)⋊C4 | C2 | semidirect |
| 41. C2×#3633 | D4 | semidirect |
| 42. C2×D4×C17 | C8 | semidirect |
| 43. C2×C22⋊D17 | C8 | semidirect |
| 44. C2×C22⋊D17 | C8 | semidirect |
| 47. C2×D68 | C8 | semidirect |
| 55. C23×C17 | C2×C8 | semidirect |
| 64. C22×D17 | C2×C8 | semidirect |
| 86. C2×C4×C17 | C2×C8 | semidirect |
| 89. C2×Dic17 | C2×C8 | semidirect |
| 97. C22×C17 | C22⋊C8 | semidirect |
| 108. C2×D17 | C22⋊C8 | semidirect |
| 150. C17 | #1869 | semidirect |
| 158. C2×D4 | #3633 | semidirect |
| 196. C23 | C2×#3633 | semidirect |
| 220. C2×C4 | C2×#3633 | semidirect |
| 240. C22 | C22⋊#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×#3633)⋊C4 | 2 |
| C2×D4×#595 | 2 |
| #1869 | 17 |