Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
528 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 215 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. #11763922 | C2 | direct (N × H) |
| 2. C2×C4⋊#3633 | C2 | semidirect |
| 4. C2×C4×#3633 | C2 | semidirect |
| 17. C4⋊#3633 | C22 | semidirect |
| 18. C4×#3633 | C22 | semidirect |
| 31. C22×C4×C17 | C8 | semidirect |
| 32. C22×Dic17 | C8 | semidirect |
| 33. C2×C4×D17 | C8 | semidirect |
| 34. C2×C4×D17 | C8 | semidirect |
| 35. C2×C4×D17 | C8 | semidirect |
| 67. C2×C4×C17 | C2×C8 | semidirect |
| 70. C2×Dic17 | C2×C8 | semidirect |
| 73. C4×D17 | C2×C8 | semidirect |
| 74. C4×D17 | C2×C8 | semidirect |
| 105. C2×C17 | #431 | semidirect |
| 108. D17 | #431 | semidirect |
| 124. C17 | C2×#431 | semidirect |
| 142. C22×C4 | #3633 | semidirect |
| 181. C2×C4 | C2×#3633 | semidirect |
| 209. C2 | #11763922 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763922 | 2 |
| C2×C4⋊#3633 | 2 |
| C2×C22⋊#3633 | 2 |
| C2×C4×#3633 | 2 |
| C22×C4×#595 | 2 |
| C2×#431 | 17 |