Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
256 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 64 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. #11763865 | C2 | semidirect |
| 2. D17⋊#108 | C2 | semidirect |
| 3. #11763727 | C2 | semidirect |
| 17. #10587535 | C22 | semidirect |
| 18. #10587530 | C22 | semidirect |
| 92. D17 | #361 | semidirect |
| 108. C17 | C2×#361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763865 | 2 |
| D17⋊#108 | 2 |
| #11763727 | 2 |
| C2×D8×D17 | 2 |
| C2×#361 | 17 |