Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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. #11763437 | C2 | semidirect |
| 4. #11762577 | C2 | semidirect |
| 5. #11762570 | C2 | semidirect |
| 6. #11762568 | C2 | semidirect |
| 31. C2×D4×C17 | Q8 | semidirect |
| 137. C17 | #2027 | semidirect |
| 145. C2×D4 | Dic34 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763437 | 2 |
| #11762814 | 2 |
| #11762712 | 2 |
| #11762577 | 2 |
| #11762570 | 2 |
| #11762568 | 2 |
| C17×#418 | 2 |
| #2027 | 17 |