Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
784 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 210 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. (C2×#595)⋊Q8 | C2 | semidirect |
| 5. C22×Q8×C17 | C4 | semidirect |
| 7. C2×Q8×D17 | C4 | semidirect |
| 11. C22×Dic34 | C4 | semidirect |
| 12. C22×Dic34 | C4 | semidirect |
| 93. C22×Q8 | #595 | semidirect |
| 101. C17 | #2310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587677 | 2 |
| (C2×#595)⋊Q8 | 2 |
| #11763752 | 2 |
| C22×Q8×D17 | 2 |
| #2310 | 17 |