Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
316 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 84 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. C2×#10587534 | C2 | semidirect |
| 2. C2×#10587533 | C2 | semidirect |
| 4. #11763683 | C2 | semidirect |
| 10. C2×M16×C17 | C4 | semidirect |
| 11. C2×#63223 | C4 | semidirect |
| 14. C2×#63218 | C4 | semidirect |
| 15. C2×#63218 | C4 | semidirect |
| 83. C8×C17 | C22⋊C4 | semidirect |
| 85. #3622 | C22⋊C4 | semidirect |
| 125. C2×M16 | #595 | semidirect |
| 134. C17 | #1809 | semidirect |
| 199. C8 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587534 | 2 |
| C2×#10587533 | 2 |
| #11763751 | 2 |
| #11763683 | 2 |
| C2×M16×D17 | 2 |
| #1809 | 17 |