Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
400 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 160 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. #11763833 | C2 | semidirect |
| 2. #11763826 | C2 | semidirect |
| 3. #11763825 | C2 | semidirect |
| 4. #11763816 | C2 | semidirect |
| 6. C4×#63243 | C2 | semidirect |
| 7. C4×#63242 | C2 | semidirect |
| 135. C17 | #2922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763833 | 2 |
| #11763826 | 2 |
| #11763825 | 2 |
| #11763816 | 2 |
| #11763783 | 2 |
| C4×#63243 | 2 |
| C4×#63242 | 2 |
| C4×#63254 | 2 |
| #2922 | 17 |