Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
312 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 71 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 | semidirect |
| 2. #11763922 | C2 | semidirect |
| 3. D4⋊#3633 | C2 | semidirect |
| 17. C4⋊#3633 | C22 | semidirect |
| 19. C4×#3633 | C22 | semidirect |
| 29. C2×D4×C17 | C8 | semidirect |
| 33. D4×D17 | C8 | semidirect |
| 35. C2×D68 | C8 | semidirect |
| 124. C17 | #1478 | semidirect |
| 132. C2×D4 | #3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763922 | 2 |
| D4⋊#3633 | 2 |
| C2×D4×#595 | 2 |
| #1478 | 17 |