Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
456 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 2. #11763849 | C2 | semidirect |
| 3. Q16×#595 | C2 | semidirect |
| 15. C2×Q16×C17 | C4 | semidirect |
| 16. C2×#63231 | C4 | semidirect |
| 17. Q16×D17 | C4 | semidirect |
| 18. Q16×D17 | C4 | semidirect |
| 21. C2×Dic68 | C4 | semidirect |
| 115. C2×Q16 | #595 | semidirect |
| 128. C17 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763877 | 2 |
| #11763849 | 2 |
| Q16×#595 | 2 |
| #11763819 | 2 |
| #11763802 | 2 |
| #11763772 | 2 |
| C2×Q16×D17 | 2 |
| #2950 | 17 |